Question

Differentiate with respect to x (3x^2-5ax+a^2)^4

Answer 1

This is a typical problem using the chain rule: if y = f(u) and u = g(x), then dy/dx = dy/du * du/dx

Here, let u = 3x^2 - 5ax + a^2
So, y = u^4
dy/du = 4u^3
du/dx = 6x - 5a

dy/dx = 4u^3 * (6x-5a)
= 4(3x^2 - 5ax + a^2)^3 * (6x-5a)

Don't let the a's bother you. They're just some number, like 3 or -4, just one we don't happen to know. Just carry them through like any other constant.