# Compute the following derivatives \frac{d}{dx}[x^{4}\tan^{3}(x^{2})]

Compute the following derivatives
$\frac{d}{dx}\left[{x}^{4}{\mathrm{tan}}^{3}\left({x}^{2}\right)\right]$
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Fatema Sutton
$y={x}^{4}{\mathrm{tan}}^{3}\left({x}^{2}\right)$
Differentiating with respect to x
${y}^{\prime }={x}^{4}×3{\mathrm{tan}}^{2}\left({x}^{2}\right)×{\mathrm{sec}}^{2}\left({x}^{2}\right)×2x+{\mathrm{tan}}^{3}\left({x}^{2}\right)×4{x}^{3}$
Used chain rule which says derivative of
F(G(X))=F'(G'(X))
${y}^{\prime }=6{x}^{5}{\mathrm{tan}}^{2}\left({x}^{2}\right){\mathrm{sec}}^{2}\left({x}^{2}\right)+4{x}^{3}{\mathrm{tan}}^{3}\left({x}^{2}\right)$