Question

How to find the derivative of:

f(x) = x^3(x − 7)^2

Answer 1

product rule is my first impression

Answer 2

product rule and chain rule

Answer 3

assuming its a product to begin with, and not a confuddled exponent

Answer 4

how would I go about starting... im sorry, i am terrible at math haha

Answer 5

\[D[fg]=f'g+fg'\]

Answer 6

x^2(5x-7)(5x-7) something like that?

Answer 7

..... maybe. but i cant see it as that yet

Answer 8

(x-7)*

Answer 9

i probably messed up, what did you get?

Answer 10

f(x) = x^3 * (x − 7)^2

f'(x) = x'^3 * (x − 7)^2 + x^3 * (x − 7)'^2

f'(x) = 3x^2 * (x − 7)^2 + x^3 * 2(x − 7)(x − 7)'

f'(x) = 3x^2 * (x − 7)^2 + x^3 * 2(x − 7)(1)

Answer 11

just follow the definition of a product rule ....

Answer 12

and notice the chain rule pops out that (x-7)'

Answer 13

yeah alright let me see