Question

Find the derivative of the function?

Answer 1

`f'(x) = -(8x + 9sqrt(x))/(2x^6)`

Explanation:

`f(x) = (x + sqrt(x))/x^5`

`= x^(-4) + x^(-9/2)`

Using the power rule,

`d/dx(x^n) = n x^(n-1)`

`f'(x) = (-4)x^(-5) + (-9/2) x^(-11/2)`

`= -(4x)/x^6 -9/2 sqrt(x)/x^6`

`= -(8x + 9sqrt(x))/(2x^6)`