If f(1)=1 and f^{prime}(1)=3,then the derivat | vedclass

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

Question

(D) Let $y = f(f(f(x))) + (f(x))^2$. Applying the chain rule,the derivative is: $\frac{dy}{dx} = f^{\prime}(f(f(x))) \cdot f^{\prime}(f(x)) \cdot f^{\

Vedclass · Accepted Answer

$33$

Vedclass · Answer

(D) Let $y = f(f(f(x))) + (f(x))^2$. Applying the chain rule,the derivative is: $\frac{dy}{dx} = f^{\prime}(f(f(x))) \cdot f^{\prime}(f(x)) \cdot f^{\prime}(x) + 2f(x)f^{\prime}(x)$. Evaluating at $x=1$: $\left. \frac{dy}{dx} \right|_{x=1} = f^{\prime}(f(f(1))) \cdot f^{\prime}(f(1)) \cdot f^{\prime}(1) + 2f(1)f^{\prime}(1)$. Given $f(1)=1$ and $f^{\prime}(1)=3$,we have: $f(f(1)) = f(1) = 1$ and $f(f(f(1))) = f(1) = 1$. Substituting these values: $\left. \frac{dy}{dx} \right|_{x=1} = f^{\prime}(1) \cdot f^{\prime}(1) \cdot f^{\prime}(1) + 2(1)(3) = 3 \cdot 3 \cdot 3 + 6 = 27 + 6 = 33$.

If $f(1)=1$ and $f^{\prime}(1)=3$,then the derivative of $f(f(f(x)))+(f(x))^2$ at $x=1$ is

Similar Questions

$\frac{d}{d x}\left(\frac{2^x+3^x}{4^x}\right) = $ . . . . . .

If $f(x) = \sin([\pi^{2}]x) + \cos([-\pi^{2}]x)$,then find $f'(x)$,where $[\cdot]$ denotes the greatest integer function.

If $f^{\prime}(x) = \tan^{-1}(\sec x + \tan x)$,$\frac{-\pi}{2} < x < \frac{\pi}{2}$ and $f(0) = 0$,then $f(1) =$

The differential of ${e^{x^3}}$ with respect to $\log_e x$ is

For the function $f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + \dots + \frac{x^2}{2} + x + 1$,prove that $f^{\prime}(1) = 100 f^{\prime}(0)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module