# How do you differentiate f(x)=sinx/(x-3)^3 using the quotient rule?

Jun 13, 2018

$y ' = \frac{\cos \left(x\right) \left(x - 3\right) - 3 \sin \left(x\right)}{x - 3} ^ 4$

#### Explanation:

Using the Quotient rule we get

$y ' = \frac{\cos \left(x\right) {\left(x - 3\right)}^{3} - \sin \left(x\right) 3 {\left(x - 3\right)}^{2}}{x - 3} ^ 6$
simplifying

$y ' = \frac{\cos \left(x\right) \left(x - 3\right) - 3 \sin \left(x\right)}{x - 3} ^ 4$