How do you find the derivative of #h(x) = (6x-x^3)^2#?

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Answer 1 · 2016-06-14T18:12:14

#y = u^2#

#u = (6x - x^3)#

The chain rule states that #dy/dx = dy/(du) xx (du)/dx#.

We must therefore differentiate both functions. Starting with #y#:

#y' = 2u^(2 - 1)#

#y' = 2u#

Now for #u#:

#u' = 6 - 3x^2#

#:. dy/dx = 2u xx (6 - 3x^2)#

#dy/dx = 2(6x - x^3) xx (6 - 3x^2)#

#dy/dx = (12x - 2x^3)(6 - 3x^2)#

#dy/dx = 72x - 12x^3 + 6x^5 - 36x^3#

#dy/dx = 6x^5 - 48x^3 + 72x#

Hopefully this helps!