my question is in the description box, please help me with this problem

Question

d/dx(u^5+u^3), where u=(3/v)-4v, and v =3-x^2, find dy/dx at x=2

Answer 1

Use the chain rule twice.

 

d/dx(g(u)) = (dg/du) (du/dv) (dv/dx)

 

g(u) = u⁵ + u³

 

u = 3/v - 4v

 

v = 3 - x²

 

dg/du = 5u⁴ + 3u²

 

du/dv = -3/v² - 4

 

dv/dx = -2x

 

d/dx(u⁵ + u³) = (5u⁴ + 3u²)(-3/v² - 4)(-2x)

 

You can simplify it further and finish from here.