# How do you find the derivative of  cos(1-2x)^2?

May 11, 2018

$4 \left(1 - 2 x\right) \sin {\left(1 - 2 x\right)}^{2}$

#### Explanation:

$\text{differentiate using the "color(blue)"chain rule}$

$\text{given "y=f(g(x))" then}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(g \left(x\right)\right) \times g ' \left(x\right) \leftarrow \textcolor{b l u e}{\text{chain rule}}$

$\Rightarrow \frac{d}{\mathrm{dx}} \left(\cos {\left(1 - 2 x\right)}^{2}\right)$

$= - \sin {\left(1 - 2 x\right)}^{2} \times \frac{d}{\mathrm{dx}} \left({\left(1 - 2 x\right)}^{2}\right)$

$= - \sin {\left(1 - 2 x\right)}^{2} \times 2 \left(1 - 2 x\right) \times \frac{d}{\mathrm{dx}} \left(1 - 2 x\right)$

$= - \sin {\left(1 - 2 x\right)}^{2} \times 2 \left(1 - 2 x\right) \times - 2$

$= 4 \left(1 - 2 x\right) \sin {\left(1 - 2 x\right)}^{2}$