Derivative/(g(f(x)))^2f(g(x))/f is x^2-1 and g is x+2/Exercise

Let

$f,g:ℝ⟶ℝ$

be two differentiable functions and consider

$h(x)=(g(f(x)){)}^{2}f(g(x)).$

a) Determine the derivative $h^{\prime }$ from the derivatives of $f$ and $g$. b) Let now

$f(x)=x^2-1\text{ and }g(x)=x+2.$

Compute $h^{\prime }(x)$ in two ways, one directly from $h(x)$ and the other by the formula of part $a)$.

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