Question

find the derivative of f(x)=(x-3)(x+2)^3

Answer 1

Using formula : \[(uv)'= u'v+v'u\]. Do it carefully.

Answer 2

do i put the exponent in front of the (x-3) or (x+2)?

Answer 3

for this function, you should think that :
\[u(x)=x-3\] and \[v(x)=(x+2)^3\]
Then using formula above

Answer 4

oh okay so i got \[1\times(x+2)^3+3(1)^2(x-3)\] is this correct?

Answer 5

No, you should study next formula : \[(h^n (x))'=n.h^{n-1}.h'\]
Do v'(x) again.

Answer 6

\[(h^n(x))'=n.h^{n−1} (x).h'(x)\]

Answer 7

so v'(x)=3(x+2)^2???

Answer 8

That is correct.

Answer 9

yes

Answer 10

so therefore would the next step be (x+2)^3+3(x+2)^2(x-3)?

Answer 11

Yup, that's the derivative. :-)

Answer 12

You can simplify it if you want

Answer 13

wouldn't that be x^3+15x^2+25x+9?

Answer 14

\[(x+2)^2(4x-7)\]

Answer 15

how'd you get that?

Answer 16

\[(x+2)^3+3(x+2)^2(x-3)=(x+2)^2 (x+2+3(x-3))=...\] it's here.