Question

How do I find the derivative of `y= ln(4 x)/x^7`?

Answer 1

`dy/dx=(1-7ln(4x))/x^8`

Explanation:

The quotient rule states that

`d/dx [(f(x))/(g(x))]=(g(x)*f'(x)-f(x)*g'(x))/([g(x)]^2)`.

Application of this rule to the given function yields :

`dy/dx=(x^7(4/(4x))-7x^6*ln(4x))/(x^7)^2`

`=(x^6(1-7ln(4x)))/x^14`

`=(1-7ln(4x))/x^8`.