# Find the derivative of this function?

Apr 24, 2017

Looks like an invite to use the Quotient Rule but I'd re-write and do this:

$= \frac{d}{\mathrm{dx}} \left({e}^{{x}^{3}} {\cos}^{3} \left({x}^{3}\right)\right)$

Product Rule

$= \frac{d}{\mathrm{dx}} \left({e}^{{x}^{3}}\right) {\cos}^{3} \left({x}^{3}\right) + {e}^{{x}^{3}} \frac{d}{\mathrm{dx}} \left({\cos}^{3} \left({x}^{3}\right)\right)$

Lots of Chain Rule here:

$= \left(3 {x}^{2} \cdot {e}^{{x}^{3}}\right) {\cos}^{3} \left({x}^{3}\right) + {e}^{{x}^{3}} \left(3 {\cos}^{2} \left({x}^{3}\right) \cdot \left(- \sin \left({x}^{3}\right)\right) \cdot 3 {x}^{2}\right)$

And gather terms:

$= 3 {x}^{2} {e}^{{x}^{3}} {\cos}^{2} {x}^{3} \left(\cos {x}^{3} - 3 \sin {x}^{3}\right)$