What is the derivative of [5x^3-4x^2)3x-2]/x^2?

Question

anonymous · Answer

Is this the equation:$${(5x^3-4x^2)(3x-2)}\over(x-2)$$

anonymous · Answer

no, its $$(5x^{3}-4x ^{2}+3x-2) \div (x ^{2})$$

anonymous · Answer

Oh sorry. Didn't read properly. (:

anonymous · Answer

Okay. There is 2 ways that you can do this. One, you simplify the equation. Or, you can use the quotient rule.

anonymous · Answer

Using the quotient rule:$$u=5x^3-4x^2+3x-2$$$$v=x^2$$$${{du}\over{dx}}=15x^2-8x+3$$$${{dv}\over{dx}}=2x$$

anonymous · Answer

i've been doing the quotient rule/chain rule? but i always get confused. would this be the set up: $$[(x ^{2})(15x ^{2}-8x+3)-(5x ^{3}-4x ^{2}+3x-2)(2x)]\div(x ^{4})$$

anonymous · Answer

Yup! That's it (:

anonymous · Answer

ok, thank you! for some reason i always wanna keep doing the chain rule after the first derivative, like making the 15x^2 a 30x, so i wasn't sure if i had to stop then or keep going lol

anonymous · Answer

Oh, that is a different case altogether. that is if say your equation is something like 2(15x^2). So if you don't multiply the 2 into the bracket, then you differentiate the 15x^2 first, followed by multiplying it by 2. Sorry couldn't think of a better example.

anonymous · Answer

no, i get what you mean. i've just been doing so many problems my brain is starting to get them mixed up. thank you again!

anonymous · Answer

no problem (: