If f is a polynomial,then the second derivati | vedclass

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

Question

(D) Let $y = f(e^x)$.First,we find the first derivative with respect to $x$ using the chain rule:$\frac{dy}{dx} = f'(e^x) \cdot \frac{d}{dx}(e^x) = f'

Vedclass · Accepted Answer

$f''(e^x)e^{2x} + f'(e^x)e^x$

Vedclass · Answer

(D) Let $y = f(e^x)$.First,we find the first derivative with respect to $x$ using the chain rule:$\frac{dy}{dx} = f'(e^x) \cdot \frac{d}{dx}(e^x) = f'(e^x)e^x$.Now,we find the second derivative by applying the product rule to $\frac{dy}{dx} = f'(e^x)e^x$:$\frac{d^2y}{dx^2} = \frac{d}{dx}(f'(e^x)e^x) = \frac{d}{dx}(f'(e^x)) \cdot e^x + f'(e^x) \cdot \frac{d}{dx}(e^x)$.Using the chain rule again for $\frac{d}{dx}(f'(e^x)) = f''(e^x)e^x$,we get:$\frac{d^2y}{dx^2} = (f''(e^x)e^x)e^x + f'(e^x)e^x$.Simplifying this,we obtain:$\frac{d^2y}{dx^2} = f''(e^x)e^{2x} + f'(e^x)e^x$.

If $f$ is a polynomial,then the second derivative of $f(e^x)$ is

Similar Questions

If $f: R \rightarrow R$ is an even function which is twice differentiable on $R$ and $f^{\prime \prime}(\pi)=1$, then $f^{\prime \prime}(-\pi)$ is equal to

If $y = x + e^x$,then $\frac{d^2x}{dy^2}$ is:

$\frac{d^2x}{dy^2} = $

Find the second order derivative of the function $\sin (\log x)$.

If $a \neq b, x \neq n \pi, n \in Z$ and $y^2 = a^2 \cos^2 x + b^2 \sin^2 x$,then $\frac{d^2 y}{dx^2} + y =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module