Question

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

• A. 10
• B. 35
• C. 33
• D. 12

Answer 1

Answer: (C)

$f(1)=1,f^{\prime }(1)=3$
$\frac{d}{dx}\left[f(f(f(x)))+(f(x){)}^2\right]$
$\left[f^{\prime }(f(f(x)))\cdot f^{\prime }f(x)\cdot f^{\prime }(x)+2f(x)\cdot f^{\prime }(x)\right]$
$=f^{\prime }(f(f(1)))f^{\prime }(f(1))\cdot f^{\prime }(1)+2f(1)\cdot f^{\prime }(1)$
$f^{\prime }(f(1))f^{\prime }(1)\cdot 3+2\cdot (1)3$
$=f^{\prime }(1)\cdot 3\cdot 3+6$
$=27+6=33$