Question

If z = f o f(x) where $f\left(x\right)=x^2$, then what is $\frac{dz}{dx}$ equal to ?

• A. $x^3$
• B. $2x^3$
• C. $4x^3$
• D. $4x^2$

Answer 1

The correct option is C $4x^3$

We know that, $fof\left(x\right)=f\left(f\right(x\left)\right)$

$\therefore z=f\left(f\right(x\left)\right)=f\left(x^2\right)$

$\Rightarrow z=x^4$

$\Rightarrow \frac{dz}{dx}=4x^3$