Maths-

General

Easy

Question

# If , then is

- Even function
- An odd function
- Neither even nor odd
- None of these

Hint:

### A function's derivative is the function whose value at x is f′. (x). The graph of a function's derivative, f(x), is connected to the graph of f. (x). If the tangent line to f(x) has a positive slope, then f′(x)>0. If f′(a) exists, then a function f(x) is said to be differentiable at a. Here we have given the function If , then we have to find is even or odd function.

## The correct answer is: An odd function

### So now we have given the function as .

- A function is "even" when f(x) = f(−x) for all x.
- A function is "odd" when −f(x) = f(−x) for all x.

Let y = f(x) be a function of x. Then, the rate of change of “y” per unit change in “x” is given by: dy / dx

Here we have given that function:

Differentiation it, we get:

Here we found the derivative of the given function. The power is odd in the derivative.

Now we will find whether the function is even or odd. Replacing x with -x, we get:

So the function is odd.

Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables. A constant function has zero derivatives. For instance, f'(x) = 0 if f(x) = 8. So the derivative function is odd.

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