Question

Differentiate.
f(x)=(x^4-3x^2+5)^3

Answer 1

3(4x^3-6x)(x^4-3x^2+5)^2

I think

Answer 2

yeah that is correct but i was wondering, why do we need to bring back the original equation into the solution?!?

Answer 3

d/d(anything)=(circle)^box

box(circle)^box-1(d/d(circle))

ALWAYS this will be true

Answer 4

It is called the chain rule and it is VERY important to understand if you plan on doing more calculus.. essentially, when you have a function of the form (x+a)^b, the (x+a) term is being multiplied by itself. You must therefore differentiate by doing (x+a)'(x+a)^(b-1)

Answer 5

take (x+a)*(x+a) for example. Observe that this is of the form (x+a)^b where b=2. Now we can differentiate by performing the chain rule on this expression, which gives: (x+a)*(x+a)'+(x+a)*(x+a)' = (x+a)(1) + (x+a)(1) = 2(x+a). Now doing the way listed in the previous post, we get the same answer! NOTE: I made an error in the end of the last post, should be b*(x+a)'(x+a)^(b-1).