can't find f'(x) for f(x) = (2x^2 + 3)^4 (3x - 1)^5

[annynickname]

Hello. In a few hours I have to take a test concerning derivatives, I understand almost everything, however I'm having a hard time trying to understand an exercise which is already solved in the book, this is the excercise

find f'(x) if f(x) = (2x^2+3)^4 (3x-1)^5

and so they solve the excercise, they apply product rule followed by the general power rule, but I'm so confused, I'm lost, I don't get it, i don't understand how they solve that excercise.

Could you please explain to me how to solve an exercise of that nature? please, with easy steps.
thank you.

 

[stapel]

find f'(x) if f(x) = (2x^2+3)^4 (3x-1)^5

...i don't understand how they solve that excercise.

Could you please explain to me how to solve an exercise of that nature?

Your book and class notes already have loads of similar exercises, starting with ones having "easy" steps, so another one probably isn't going to fix the problem. Instead, we need to find where you're going astray. So let's start simple.

Can you differentiate the following?

. . . . .a(x) = 2x[sup:2puthakm]2[/sup:2puthakm] + 3

. . . . .b(x) = (2x[sup:2puthakm]2[/sup:2puthakm] + 3)[sup:2puthakm]4[/sup:2puthakm]

. . . . .c(x) = (2x[sup:2puthakm]2[/sup:2puthakm] + 3)(3x - 1)

Please show all your steps. Thank you!

Eliz.

 

[PAULK]

find f'(x) if f(x) = (2x^2+3)^4 (3x-1)^5

and so they solve the exercise, they apply product rule followed by the general power rule, but I'm so confused, I'm lost, I don't get it, i don't understand how they solve that excercise.

Could you please explain to me how to solve an exercise of that nature? please, with easy steps.
thank you.

If you have something big and messy, then break it up into (small and messy?) pieces.

The product rule says:

f' = ()() + ()()
now take the first factor:

Differentiate (2x^2+3)^4 , using whatever. (In this case the chain rule.)

Differentiate (3x-1)^5, using....

Now put the pieces into the pattern. This way, you don't have to overload your brain (or your paper).