- #1
chaosblack
- 16
- 0
Homework Statement
Find [tex]\frac{dy}{dx}[/tex] if y = [tex]\sqrt{5u^2 -3}[/tex] and u = [tex]\frac{2x}{3x+1}[/tex]
Homework Equations
Chain Rule
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{du}[/tex] x [tex]\frac{du}{dx}[/tex]
The Attempt at a Solution
[tex]\frac{dy}{du}[/tex] = 5u(5u^2 - 3)^-1/2
[tex]\frac{du}{dx}[/tex] = -6x(3x+1)^-2
[tex]\frac{dy}{dx}[/tex] = 5u(5u^2 - 3)^-1/2 x -6x(3x+1)^-2
= -30xu(5u^2 - 3)^-1/2 x (3x+1)^-2
= [tex]\frac{-60x^2}{3x+1}[/tex](5([tex]\frac{2x}{3x+1}[/tex])^2 - 3)^-1/2 x (3x+1)^-2
Is that the final simplified answer?