Question

How do you find the derivative of `[e^(1/2x)]/(2x^3)`?

Answer 1

Use the rule for the derivative of the products of tho functions:

`d(f*g)/dx = g*df/dx + f * dg/dx`

Explanation:

`(e^(1/2x))/(2x^3) =1/2x^(-3)e^(1/2x)`

`d/dx((e^(1/2x))/(2x^3)) = e^(1/2x)*d((1/2x^(-3)))/dx + 1/2x^(-3)*d(e^(1/2x))/dx =`

`= -3/2x^(-4)e^(1/2x)+1/4x^(-3)e^(1/2x) = e^(1/2x)/(4x^4)(x-6)`