# How do you find the differential dy of the function y=2x-cot^2x?

Apr 12, 2017

For $y = f \left(x\right)$, the differential of $y$ is $\mathrm{dy} = f ' \left(x\right) \mathrm{dx}$

#### Explanation:

In this question we have $f ' \left(x\right) = 2 x - {\cot}^{2} x$

so

$f ' \left(x\right) = 2 - 2 \cot x \cdot \frac{d}{\mathrm{dx}} \left(\cot x\right) = 2 - 2 \cot x \cdot \left(- {\csc}^{2} x\right)$

$f ' \left(x\right) = 2 + 2 \cot x {\csc}^{2} x$

And so, $\mathrm{dy} = \left(2 + 2 \cot x {\csc}^{2} x\right) \mathrm{dx}$