(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find [tex]\frac{dy}{dx}[/tex] if y = [tex]\sqrt{5u^2 -3}[/tex] and u = [tex]\frac{2x}{3x+1}[/tex]

2. Relevant equations

Chain Rule

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{du}[/tex] x [tex]\frac{du}{dx}[/tex]

3. 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?

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# Homework Help: Finding the derivative.

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