Question

What is the derivative of (2x-3)^3? I'm trying to use the power rule but I'm not sure where to start.

Answer 1

u know the power rule.?

Answer 2

You will also have to use the chain rule.

Answer 3

Yes I do, I just don't know how to apply it to quantities.

Answer 4

3(2x-3)^2*d/dx(2x-3)

Answer 5

thats 6(2x-3)^2

Answer 6

@amriju Why did you multiply that by d/dx(2x-3)?

Answer 7

First take the derivative of the outside, and keep the inside
3(2x-3)^2 . . .
Then multiply that by the derivative of the inside which is 2
3(2x-3)^2*2= 6(2x-3)^2 like amriju said

Answer 8

The chain rule: \[\frac{ d }{ dx } [f(g(x))]=f'(g(x))g'(x)\] g(x) would = 2x-3 and f(x)=x^3

Answer 9

@guest1234 Ok, I think I understand that know.

Answer 10

the derivative of 2x-3 is 2 and the derivative of f(x)= x^3 is 3x^2 so you can just plug it in from there. 3(2x-3)^2 (2)

Answer 11

I got it, thank you all very much!

Answer 12

your answer should be

6(2x-3)^2

Answer 13

look u have done derivatives of functions like log x...sin x...a^x...x^a..rite...what if x is replaced by f(x)..?then what u do is just do what u have done if it was jst x...and then multiply to it the derivative of f(x)...ex.:
d/dx(log(x^2))
derivative of log x is 1/x....so here u just take derivative of log x^2 is 1/x^2...but since its not x...what u do is jst multiply dat with derivative of x^2....2x...so ans is..1/x^2*2x=2/x....

Answer 14

common for any function...