# If f(x)= sin(- x -1)  and g(x) = 4x^2 -5 , how do you differentiate f(g(x))  using the chain rule?

Mar 23, 2016

$\frac{d}{\mathrm{dx}} \left(f \left[g \left(x\right)\right]\right) = - 8 x \cos \left(5 - 4 {x}^{2}\right)$

#### Explanation:

$f \left[g \left(x\right)\right] = f \left(4 {x}^{2} - 5\right)$

$= \sin \left[- \left(4 {x}^{2} - 5\right)\right]$

$= \sin \left(5 - 4 {x}^{2}\right)$

$\therefore \frac{d}{\mathrm{dx}} \left[\sin \left(5 - 4 {x}^{2}\right)\right] = - 8 x \cos \left(5 - 4 {x}^{2}\right)$