Question

Find the derivative. Please show your process. F(x)= 2/sqrt(x) + sqrt(x)/2

Answer 1

Using power rule alone, you have


`(\mathrm d)/(\mathrm dx)\left[\frac2{\sqrt x}+\frac{\sqrt x}2\right]=(\mathrm d)/(\mathrm dx)\left[2x^(-1/2)+\frac12x^(1/2)\right]=-x^(-3/2)+\frac14x^(-1/2)=-\frac14x^(-3/2)(4-x)`