Question

Differentiate with respect to x.

2(2x+1)^3

Answer 1

\[\large{\frac{d}{dx}(2(2x+1)^3)}\]

Answer 2

\[\large{2\frac{d}{dx}(2x+1)^3}\]

Answer 3

m i wrong @JayDS ?

Answer 4

Now we have to use chain rule

Answer 5

that states that:
\[\large{\frac{d}{dx}((2x+1)^3) =\frac{du^3}{du}*\frac{du}{dx}}\]

where u = 2x+1 and \(\frac{du^3}{du}=3u^2\)

Answer 6

wait, I'm confused, I think I was taught another way to differentiate.

Answer 7

so what we have now is :
\[\large{2(3(2x+1)^2 * \frac{d}{dx}(2x+1)}\]
\[\large{2(3(2x+1)^2*2\frac{d}{dx}x +0}\]

Answer 8

\[\large{6*2(2x+1)^2=12(x+1)^2}\]

Answer 9

where r u having problem in understanding this @JayDS ??

Answer 10

all of it.

Answer 11

hmn..

do you know chain rule?

Answer 12

nope.

Answer 13

2(2x+1)^3 => 2*3(2x+1)^2 * 2 => ...

Answer 14

@shubham.bagrecha u took that problem as wrong..

it is 2 * (2x+1)^3 not {2(2x+1)}^3

Answer 15

hmn jayDS you must know chain rule first

Answer 16

=> 6*2(2x+1)^2

Answer 17

@mathslover i have done that only

Answer 18

http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html

Answer 19

ok, lets say one of the example they used of y=(3x + 1)^2

D(3x + 1)^2 = 2(3x+1)^2-1 D(3x + 1)
= 2 (3x+1) (3)
= 6 (3x+1)

but why do we have to use it D(3x+1) and why is it not raised to the power of 2? I'm confused.

Answer 20

@mathslover

Answer 21

wait lemme explain u ..

Answer 22

\[\large{\frac{d}{dx}(3x+1)^2 = \frac{d}{dx}(9x^2+6x+1) }\]
\[\large{\frac{d}{dx}(9x^2)+\frac{d}{dx}(6x)+\frac{d}{dx}(1)}\]
\[\large{9\frac{d}{dx}(x^2)+6\frac{d}{dx}(x) + 0}\]
\[\large{9 * 2x + 6 (1) + 0 }\]
\[\large{18x+6}\]

Answer 23

wait, I found out it is the derivative of the inside so therefore is just 3x + 1 but why do we use it?

Answer 24

and sorry for my stupid question but why is it just d/dx, is it the same as dy=dx?

Answer 25

d/dx means that we are differentiating a term with restect to x

Answer 26

*respect

Answer 27

ok, got it, I believe I know how to do it now and I blame my teacher for providing some exercises from another book that contain this stuff that she hasn't even taught us.

Answer 28

and thanks.

Answer 29

hmn no need to blame the teacher dude

we are here... that is because openstudy is made

Answer 30

haha yeh, that's why I appreciate the admin, website and people who help me on it. thankyou.