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Question: find the derivative functions f(x)=(5x^2-4x)^2

Use the chain rule.

Let u = 5x^2 - 4x

then du/dx = 10x - 4

f = f(u) = u^2

and df/du = 2u.

We want df/dx, and by the chain rule, df/dx = (df/du)*(du/dx)


df/dx = (df/du)*(du/dx) = 2u*(10x - 4)

df/dx = 2*(5x^2 - 4x)*(10x - 4)

df/dx = 2x(5x - 4)(10x - 4)

by Level 11 User (81.5k points)

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