Question

y=4x^3(2x+1)^2 find dy/dx

Answer 1

\[y= 4x^3 * (2x+1)^2\]

Answer 2

Was just about to ask, lol. Alright, product rule then : )

Answer 3

yeah do i just find the derrivate for all of them

Answer 4

and for the y i just put y prime

Answer 5

So we will need to do:
\[f'(x)g(x) + f(x)g'(x)\]
\[f(x) = 4x^{3}\]
\[g(x) = (2x+1)^{2}\]

If you know how to get the derivativesof f(x) and g(x), you can plug it all into the product rule formula I posted :3

Answer 6

it will be

Answer 7

12x^2 * (2x+1)^2 + 4x^3 * 2(2x+1) (2)

Answer 8

Perfect ^_^ Unless you feel like cleaning it up a little bit, thats the answer.

Answer 9

but the question ask for dy/dx tho

Answer 10

does y become dy/dx?

Answer 11

because i take derivate of everything

Answer 12

That is dy/dx. And yes, it does. Youre technically takign the derivative of both sides of the equation
y = 4x^3(2x+1)^2
the derivative of y on the left is dy/dx

Answer 13

how would u clean that up btw would it be like

12x^2(2x+1)^2 + 4x^3 (8x+4)?

Answer 14

Yeah, pretty much. Without actually multiplying things out i would leave it something like that.

Answer 15

thank you so much !!!!

Answer 16

Yep, np.

Answer 17

i am new to this website
if i want to post another question, how would i go about doing so?

Answer 18

You can just close this question and then post a new one in the same way you posted this one.

Answer 19

ok :D thanks !!
will do

Answer 20

Mhm.

Answer 21

hi john.