Maths-

General

Easy

Question

The derivative of $e to the power of x cubed end exponent$ with respect to log is

$e^{x^{3}}$
$3 x^{2} 2 e^{x^{3}}$
$3 x^{3} e^{x^{3}}$
$3 x^{2} e^{x^{3}} + 3 x^{2}$

The correct answer is: $3 x cubed e to the power of x cubed end exponent$

Let $y equals e to the power of x cubed end exponent comma z equals log invisible function application x$
On differentiating w.r.t. $straight X$ , we get
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator d y over denominator d x end fraction equals e to the power of x cubed end exponent open parentheses 3 x squared close parentheses equals 3 x squared e to the power of x cubed end exponent text and end text fraction numerator d z over denominator d x end fraction equals 1 over x end cell row cell therefore fraction numerator d y over denominator d z end fraction equals fraction numerator fraction numerator d y over denominator d x end fraction over denominator fraction numerator d z over denominator d x end fraction end fraction equals fraction numerator 3 x squared e to the power of x cubed end exponent over denominator open parentheses 1 over x close parentheses end fraction equals 3 x cubed e to the power of x cubed end exponent end cell end table$

The derivative of $sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 2 x over denominator 1 plus x squared end fraction close parentheses$ with respect to $cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 minus x squared over denominator 1 plus x squared end fraction close parentheses$ is

maths-General

General

maths-

The rate of change of $square root of open parentheses x squared plus 16 close parentheses end root$ with respect to $fraction numerator x over denominator x minus 1 end fraction$ at $x equals 3$ is

maths-General

General

maths-

If $x equals a cos to the power of 4 invisible function application theta comma y equals a sin to the power of 4 invisible function application theta$ then $dy over dx text at end text theta equals fraction numerator 3 pi over denominator 4 end fraction$ is

maths-General

General

Maths-

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

Maths-General

In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.

General

maths-

The domain of the function $f open parentheses x close parentheses equals fraction numerator cos to the power of negative 1 end exponent invisible function application x over denominator left square bracket x right square bracket end fraction$ is

maths-General

General

maths-

Range of the function $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 2 end exponent plus 1 end fraction$ is

maths-General

General

maths-

The domain of the function $f open parentheses x close parentheses equals fraction numerator sin to the power of 1 end exponent invisible function application left parenthesis x minus 3 right parenthesis over denominator square root of 9 minus x to the power of 2 end exponent end root end fraction$ is

maths-General

General

maths-

Let $f open parentheses x close parentheses equals fraction numerator 1 over denominator 2 end fraction minus tan invisible function application open parentheses fraction numerator pi x over denominator 2 end fraction close parentheses$ , $negative 1 less than x less than 1$ and $g open parentheses x close parentheses equals square root of 3 plus 4 x minus 4 x to the power of 2 end exponent end root$ , then dom $left parenthesis f plus g right parenthesis$ is given by

maths-General

General

physics-

In the adjacent diagram, $C P$ represents a wavefront and $A O$ and $B P$ , the corresponding two rays. Find the condition on $theta$ for constructive interference at P between the ray $B P$ and reflected ray $O P$

physics-General

General

chemistry-

Select the rate law that correspond to the data shown for the following reaction.

chemistry-General

General

chemistry-

Select the rate law that corresponds to the data shown for the following reaction.

chemistry-General

General

maths-

$R$ is relation on $N$ given by $R equals left curly bracket open parentheses x comma blank y close parentheses colon 4 x plus 3 y equals 20 right curly bracket$ Which of the following belongs to $R$ ?

maths-General

General

physics-

Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison with the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle $theta$ under the influence of magnets. The ratio of distances d₁ and d₂ will be

physics-General

General

physics-

Two small magnets X and Y of dipole moments M₁ and M₂ are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is

physics-General

General

physics-

Find the resultant magnetic moment for the following arrangement

physics-General

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The derivative of with respect to log is

The correct answer is:

Let On differentiating w.r.t. , we get

Related Questions to study

The derivative of with respect to is

The derivative of with respect to is

The rate of change of with respect to at is

The rate of change of with respect to at is

If then is

If then is

If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is

If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is

The domain of the function is

The domain of the function is

Range of the function is

Range of the function is

The domain of the function is

The domain of the function is

Let , and , then dom is given by

Let , and , then dom is given by

In the adjacent diagram, represents a wavefront and and , the corresponding two rays. Find the condition on for constructive interference at P between the ray and reflected ray

In the adjacent diagram, represents a wavefront and and , the corresponding two rays. Find the condition on for constructive interference at P between the ray and reflected ray

Select the rate law that correspond to the data shown for the following reaction.

Select the rate law that correspond to the data shown for the following reaction.

Select the rate law that corresponds to the data shown for the following reaction.

Select the rate law that corresponds to the data shown for the following reaction.

is relation on given by Which of the following belongs to ?

is relation on given by Which of the following belongs to ?

Two small magnets X and Y of dipole moments M1 and M2 are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is

Two small magnets X and Y of dipole moments M1 and M2 are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is

Find the resultant magnetic moment for the following arrangement

Find the resultant magnetic moment for the following arrangement

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The derivative of $e to the power of x cubed end exponent$ with respect to log is

The correct answer is: $3 x cubed e to the power of x cubed end exponent$

The rate of change of $square root of open parentheses x squared plus 16 close parentheses end root$ with respect to $fraction numerator x over denominator x minus 1 end fraction$ at $x equals 3$ is

The rate of change of $square root of open parentheses x squared plus 16 close parentheses end root$ with respect to $fraction numerator x over denominator x minus 1 end fraction$ at $x equals 3$ is

If $x equals a cos to the power of 4 invisible function application theta comma y equals a sin to the power of 4 invisible function application theta$ then $dy over dx text at end text theta equals fraction numerator 3 pi over denominator 4 end fraction$ is

If $x equals a cos to the power of 4 invisible function application theta comma y equals a sin to the power of 4 invisible function application theta$ then $dy over dx text at end text theta equals fraction numerator 3 pi over denominator 4 end fraction$ is

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

The domain of the function $f open parentheses x close parentheses equals fraction numerator cos to the power of negative 1 end exponent invisible function application x over denominator left square bracket x right square bracket end fraction$ is

The domain of the function $f open parentheses x close parentheses equals fraction numerator cos to the power of negative 1 end exponent invisible function application x over denominator left square bracket x right square bracket end fraction$ is

Range of the function $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 2 end exponent plus 1 end fraction$ is

Range of the function $f open parentheses x close parentheses equals fraction numerator x to the power of 2 end exponent over denominator x to the power of 2 end exponent plus 1 end fraction$ is

In the adjacent diagram, $C P$ represents a wavefront and $A O$ and $B P$ , the corresponding two rays. Find the condition on $theta$ for constructive interference at P between the ray $B P$ and reflected ray $O P$

In the adjacent diagram, $C P$ represents a wavefront and $A O$ and $B P$ , the corresponding two rays. Find the condition on $theta$ for constructive interference at P between the ray $B P$ and reflected ray $O P$

$R$ is relation on $N$ given by $R equals left curly bracket open parentheses x comma blank y close parentheses colon 4 x plus 3 y equals 20 right curly bracket$ Which of the following belongs to $R$ ?

$R$ is relation on $N$ given by $R equals left curly bracket open parentheses x comma blank y close parentheses colon 4 x plus 3 y equals 20 right curly bracket$ Which of the following belongs to $R$ ?

Two small magnets X and Y of dipole moments M₁ and M₂ are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is

Two small magnets X and Y of dipole moments M₁ and M₂ are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is