How do you use the chain rule to differentiate y=(5x^4+1)^2y=(5x4+1)2?

1 Answer
May 1, 2017

dy/dx=200x^7+40x^3dydx=200x7+40x3

Explanation:

d/dx(f(g(x)))=f'(g(x))xxg'(x)larr" chain rule"

"here "f(g(x))=(5x^4+1)^2

g(x)=5x^4+1

y=(5x^4+1)^2

rArrdy/dx=2(5x^4+1)xxd/dx(5x^4+1)

color(white)(rArrdy/dx)=2(5x^4+1)xx20x^3

color(white)(rArrdy/dx)=40x^3(5x^4+1)

color(white)(rArrdy/dx)=200x^7+40x^3