Maths-
General
Easy

Question

The value of fraction numerator d over denominator d x end fraction open square brackets open parentheses fraction numerator tan squared invisible function application 2 x minus tan squared invisible function application x over denominator 1 minus tan squared invisible function application 2 x tan squared invisible function application x end fraction close parentheses cot invisible function application 3 x close square brackets is

  1. tan invisible function application 2 x tan invisible function application x
  2. tan invisible function application 3 x tan invisible function application x
  3. sec squared invisible function application x
  4. sec invisible function application x tan invisible function application x

The correct answer is: sec squared invisible function application x


    Let,y equals fraction numerator tan squared invisible function application 2 x minus tan squared invisible function application x over denominator 1 minus tan squared invisible function application 2 x tan squared invisible function application x end fraction
    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 equals fraction numerator left parenthesis tan invisible function application 2 x minus tan invisible function application x right parenthesis over denominator left parenthesis 1 plus tan invisible function application 2 x tan invisible function application x right parenthesis end fraction times fraction numerator left parenthesis tan invisible function application 2 x plus tan invisible function application x right parenthesis over denominator left parenthesis 1 minus tan invisible function application 2 x tan invisible function application x right parenthesis end fraction end cell row cell equals tan invisible function application left parenthesis 2 x minus x right parenthesis tan invisible function application left parenthesis 2 x plus x right parenthesis end cell row cell equals tan invisible function application x tan invisible function application 3 x end cell end table

    On differentiating w.r.t. 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 over denominator d x end fraction left parenthesis y times cot invisible function application 3 x right parenthesis equals fraction numerator d over denominator d x end fraction left parenthesis tan invisible function application x tan invisible function application 3 x cot invisible function application 3 x right parenthesis end cell row cell equals fraction numerator d over denominator d x end fraction left parenthesis tan invisible function application x right parenthesis end cell row cell equals sec squared invisible function application x end cell end table

    Related Questions to study

    General
    maths-

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

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

    maths-General
    General
    maths-

    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

    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

    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
    parallel
    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

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

    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
    parallel
    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

    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

    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

    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
    parallel
    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 Pand 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 Pand reflected ray O P

    physics-General
    General
    chemistry-

    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.

    chemistry-General
    General
    chemistry-

    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.

    chemistry-General
    parallel
    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?

    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

    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

    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
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.