Chain rule for composite functions

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Exercises

  1. Apply the chain rule to compute derivatives like $\frac{d}{dx}[f(3x)]^2$, $\frac{d}{dx}\tan[f(x)]^2$.
  2. Compute $g’(1)$ taking into account that $f(1) = 1$ and $f’(1) = 3$ for functions like $g(x) = x^2 + f(x)$, $g(x) = x^2f(x)$.
  3. Compute the following derivatives.
    1. a) $\frac{d}{dx}[2f(3f(x))]$
    2. b) $\frac{d}{dx}[e^{[f(x)]^{2+5}}]$