Derivatives and simplifying

Question

Hello,

I've been trying to solve 12/(5(7x^4-2x)^5) with chain rule to find the derivative and I can find the part at the top without problem but the bottom is another story because at the bottom there is a part where (7x^4-2x)^6 needs to be simplified and in the answer I have in my book it is simplified to x^6(7x^3-2)^6 but how I don't understand I know they took out the x but why is x to the power 6 and why is the inner function (7x^3-2) to the power 6 as well. I may be missing some kind of rule and thats probably the case but I just can't figure out what I'm missing please help.

Answer 1

Let u = (7x^4-2x)

d/dx (12/(5(7x4-2x)^5) = 12/5 d/dx (7x^4-2x)^-5 = 12/5 d/du (u^-5) du/dx

= (12/5)(-5u^-6) d/dx (7x^4-2x)

= (-12/u^6) (28x^3 - 2)

= -12(28x^3-2)/(7x^4-2x)^6