# How do you differentiate f(x)=csc(1/(5x^2-1)) using the chain rule?

$\frac{d}{\mathrm{dx}} \csc \left(\frac{1}{5 {x}^{2} - 1}\right) = - \csc \left(\frac{1}{5 {x}^{2} - 1}\right) \cdot \cot \left(\frac{1}{5 {x}^{2} - 1}\right) \cdot \frac{- 10 x}{5 {x}^{2} - 1} ^ 2$
$\frac{d}{\mathrm{dx}} \csc \left(\frac{1}{5 {x}^{2} - 1}\right) = - \csc \left(\frac{1}{5 {x}^{2} - 1}\right) \cdot \cot \left(\frac{1}{5 {x}^{2} - 1}\right) \cdot \frac{- 10 x}{5 {x}^{2} - 1} ^ 2$