Question

If $f\left(1\right)=1,f^{\prime }\left(1\right)=3$, then the value of derivative of $f\left(f\right(fx\left)\right))+(f\left(x\right){)}^2$ at $x=1$ is?

• A. $9$
• B. $33$
• C. $12$
• D. $20$

Answer 1

Answer: (B)

$33$

$y=f\left(f\right(f\left(x\right))+(f\left(x\right){)}^2$
$\frac{dy}{dx}=f^{\prime }\left(f\right(f\left(x\right))\cdot f^{\prime }(f\left(x\right))\cdot f^{\prime }(x)+2f(x\left)f^{\prime }\right(x)$
Put $x=1\Rightarrow f^{\prime }\left(f\right(f\left(1\right)\left)\right)\cdot f^{\prime }\left(f\right(1\left)\right)\cdot f^{\prime }\left(1\right)+2f\left(1\right)\cdot f^{\prime }\left(1\right)=27+6=33$.