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)