If f(x) is an even function, then write whether f'(x) is even of … - Vidyadip

Question

If f(x) is an even function, then write whether f'(x) is even of odd.

✓

Answer

Here,
f(x) is even function, so
f(-x) = f(x)
Differentiating it with respect to x,
$\frac{\text{d}}{\text{dx}}(\text{f}(-\text{x}))=\frac{\text{d}}{\text{dx}}(\text{f}(\text{x}))$
$\text{f}'(-\text{x})\frac{\text{d}}{\text{dx}}(-\text{x})=\text{f}'\text{(x)}$
$\text{f}'(-\text{x})\times(-1)=\text{f}'(\text{x})$
$-\text{f}'(-\text{x})=\text{f}'(\text{x})$
$\text{f}'(-\text{x})=-\text{f}'(\text{x})$
So,
f'(x) is odd function.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evalute the following integrals:
$\int\frac{\sec\text{x cosec x}}{\log(\tan\text{x})}\text{dx}$

Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.

$\text{f}(\text{x})=\sin\text{x}-\sin2\text{x}-\text{x}\text{ on }[0,\pi]$

Find the principal value of the following:
$\sec^{-1}\Big(2\sin\frac{3\pi}{4}\Big)$

In $\left[\begin{array}{cc}x+y & 2 \\ 5+z & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$ find the value of $x, y, z$ ?

A function f(x) is defined as,
$\text{f}\text{(x)}=\begin{cases}\frac{\text{x}^2-\text{x}-6}{\text{x}-3}&; &\text{if} \text{x}\neq3\\5 &;&\text{if}\text{ x}=3\end{cases}$
show that f(x) is continuous that x = 3.

Solve the following equation
$\text{xy dy}=(\text{y}-1)(\text{x}+1)\text{dx}$

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, -1) and (4, 3, -1).

By using properties of determinants, show that:
$\begin{vmatrix}y+k&y&y\\y&y+k&y\\y&y&y+k\end{vmatrix}=k^2(3y+k)$

If A is a 3 × 3 matrix, |A| ≠ 0 and |3A| = |A| then write the value of k.

Find the area of the triangle with vertices at the points:
(0, 0), (6, 0) and (4, 3)