If f(x) is an odd differentiable function def | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that $f(x)$ is an odd differentiable function. By definition of an odd function, $f(-x) = -f(x)$. Differentiating both sides with respect to

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Given that $f(x)$ is an odd differentiable function. By definition of an odd function, $f(-x) = -f(x)$. Differentiating both sides with respect to $x$ using the chain rule: $\frac{d}{dx}[f(-x)] = \frac{d}{dx}[-f(x)]$ $-f^{\prime}(-x) = -f^{\prime}(x)$ $f^{\prime}(-x) = f^{\prime}(x)$ This shows that the derivative of an odd function is an even function. Now, substitute $x = 3$ into the equation $f^{\prime}(-x) = f^{\prime}(x)$: $f^{\prime}(-3) = f^{\prime}(3)$ Since it is given that $f^{\prime}(3) = 2$, we have: $f^{\prime}(-3) = 2$.

If $f(x)$ is an odd differentiable function defined on $(-\infty, \infty)$ such that $f^{\prime}(3)=2,$ then $f^{\prime}(-3)$ is equal to

Similar Questions

If $y=\sqrt{2 x+\cos ^2\left(2 x+\frac{\pi}{4}\right)}$,then find $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$.

Suppose for a differentiable function $h$,$h(0)=0$,$h(1)=1$ and $h^{\prime}(0)=h^{\prime}(1)=2$. If $g(x)=h(e^{x}) e^{h(x)}$,then $g^{\prime}(0)$ is equal to:

If $f$ and $g$ are differentiable functions such that $g'(a) = 2$ and $g(a) = b$,and if $f \circ g$ is an identity function,then $f'(b)$ has the value equal to:

If $y=x^x+x^7+7^x+7^7$,then $\frac{dy}{dx}=$

Let $f(x) = (x^x)^x$ and $g(x) = x^{(x^x)}$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module