# How do you find the derivative of cos(pi*x^2)?

Dec 16, 2016

$- 2 \pi x \sin \left(\pi {x}^{2}\right)$

#### Explanation:

differentiate using the $\textcolor{b l u e}{\text{chain rule}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(\cos \left(f \left(x\right)\right)\right) = - \sin \left(f \left(x\right)\right) . f ' \left(x\right)}} \textcolor{w h i t e}{\frac{2}{2}} |}}$

$\Rightarrow \frac{d}{\mathrm{dx}} \left[\cos \left(\pi {x}^{2}\right)\right] = - \sin \left(\pi {x}^{2}\right) . \frac{d}{\mathrm{dx}} \left(\pi {x}^{2}\right)$

$= - 2 \pi x \sin \left(\pi {x}^{2}\right)$