Chain Rule

Question

Use chain rule to find the following derivative:

((t-3)^2) / ((t+1)^1/2)

Answer 1

Given rational expression is (t-3)^2/(t+1)^1/2

= (t-3)^2*(t+1)^-1/2

Recall the formula d/dx(uv) = uv'+vu'

= d/dx((t-3)^2*(t+1)^-1/2)

= (t-3)^2 d/dx((t+1)^-1/2)+(t+1)^-1/2 d/dx(t-3)^2

= (t-3)^2(-1/2(t+1)^-3/2*1)+(t+1)^-1/2(2((t-3)*1)

= -((t-3)^2(t+1)^-3/2)/2+(t+1)^-1/2(2t-6)