How do you use the chain rule to differentiate #y=(5x^5-4x^3)^-3#?

Question

1510 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-30T21:46:49

#dy/dx=(-30x+36x^2)/(5x^2-4x^3)^4#

#y=(5x^2-4x^3)^-3#

Differentiate

#dy/dx=-3(5x^2-4x^3)^-4* color(green)(d/dx(5x^2-4x^3)color(blue)(rarr "Chain Rule")#

#dy/dx=-3(5x^2-4x^3)^-4*(10x-12x^2)#

Simplify

#dy/dx=(-30x+36x^2)/(5x^2-4x^3)^4#