Question

How do you take the derivative of d/dx [3x(x^2+1)^3] using the chain rule?

Answer 1

\[\huge \frac{d}{dx}[3x(x^2+1)^3] \]
this problem?

Answer 2

yes

Answer 3

\[\huge \frac{d}{dx}[3x(x^2+1)^3] \]
\[\huge =3\frac{d}{dx}[x(x^2+1)^3] \]
\[\huge =3\cdot([x]'(x^2+1)^3+x[(x^2+1)^3]') \]
\[\huge =3\cdot(1\cdot(x^2+1)^3+x\cdot 3(x^2+1)^2\cdot [x^2+1]') \]
can you take it from here?

Answer 4

that last line should read:
\[\large =3\cdot(1\cdot(x^2+1)^3+x\cdot 3(x^2+1)^2\cdot [x^2+1]') \]

Answer 5

okay thanks. let me see if I can work it out.

Answer 6

ok...:)
tag me if you still need help...

Answer 7

okay i got as far as 3(x^2+1)^3 + 18x^2(x^2+1)^2 but my book says the answer is 3(x^2+1)^2(7x^2+1). Im confused as to how it simplifies to that final answer

Answer 8

\(\large =3\cdot(1\cdot(x^2+1)^3+x\cdot 3(x^2+1)^2\cdot [x^2+1]') \)
\(\large =3\cdot(1\cdot(x^2+1)^3+x\cdot 3(x^2+1)^2\cdot (2x) \)
\(\large =3\cdot((x^2+1)^3+6x^2(x^2+1)^2) \)
\(\large =3(x^2+1)^2((x^2+1)+6x^2) \)
\(\large =3(x^2+1)^2(7x^2+1) \)