Question

y= x(2x+1)^3 find derivate.

Answer 1

derivative?

Answer 2

derivative

Answer 3

Do you know the product rule? Do you know the chain rule?

Answer 4

I can explain them if you don't.

Answer 5

yes , I need help

Answer 6

Product rule is used when you are taking the derivative of two things multiplied together. The rule says this:
The derivative of a*b is
a'*b + b'*a

Answer 7

yes, I know

Answer 8

Haha that's why I asked if you knew.

Answer 9

You know chain rule?

Answer 10

the problem is i can't the answer

Answer 11

derivative of f(g(x)) is
f'(g(x))*g'(x)

Answer 12

In this case, the two things multiplied together are x and (2x+1)^3
So product rule tells me the derivative will be
(derivative of x) * (2x+1)^3
+ (derivative of (2x+1)^3)*x

Answer 13

Do you know derivative of x?

Answer 14

is 1

Answer 15

And can you take the derivative of (2x+1)^3? It requires chain rule.

Answer 16

is 6(2x+1)^2

Answer 17

nicely done.

Answer 18

So product rule is all you need now.

Answer 19

but, I don't know the other value (8x+1)

Answer 20

? What.

Answer 21

Just do product rule
(Derivative of 1st thing) *(second thing) + (Derivative of second thing)*(first thing)

You've taken the derivative of x and you've taken the derivative of (2x+1)^3, so you have everything you need.