Question

Differentiate the following:
f(x)=x(2x-5)^3

Answer 1

let x=u and v= (2x-5)^3

dy/dx = vu' + uv'

Answer 2

So, I know I have the product rule and the chain rule that need to be applied here.

Answer 3

yeah so what's the problem if u know how to do it

Answer 4

Right. So i did dy/dx = dy/du*du/dx

Answer 5

Where u = 2x-5 and y= x*u^3

Answer 6

So then I get the following:

Answer 7

d/du(x*u^3) * d/dx(2x-5)

Answer 8

And then I have to apply the product rule to x*u3, right?

Answer 9

So that would be as follows: x*d/du(u^3)+d/dx(x)*(u^3)

Answer 10

u're making this soo long...u should just apply the formula i wrote above in the first place

Answer 11

I'm doing it how the professor showed us. I think she wants us to use substitution on the test. She's VERY specific.

Answer 12

Let me try it your way, though.

Answer 13

Give me a minute to see what I get?

Answer 14

Please?

Answer 15

your formula gives me (2x-5)^3+3x(2x-5)^2

Answer 16

Substitution? I associate substitution with integration, the oppositie of differentiation.

Arqum's differentiation formula (the product rule) is correct.

Answer 17

yeah i know how professors can be... ok so im going to solve it for u

u=x v=(2x-5)^3
u'=1 v'=6(2x-5)^2
dy/dx = vu' + uv'
=(2x-5)^3 (1) + x(6)(2x-5)^2

so yeah your answer seems correct just take common and blingidy u have your answer

Answer 18

So when I do it your way, I completely miss doing the derivative of 2x-3.
When I do it the professor's way, it doesn't reduce.

Answer 19

The derivative of 2x-5 is 2..

Answer 20

You could, if you wanted to, factor (2x-5) out of this expression. Try it.

Answer 21

yes when you find out the value of v' that is differentiation of (2x-5)^3 u have to differentiate 2x-5 too

Answer 22

(2x-5)^2(2x-5)+6x which is (2x-5)^2(8x-5)

Answer 23

I feel like I always forget something. Would you guys mind showing me the substitution method?

Answer 24

I can't figure out why I don't get the same answer. I must be subbing wrong.

Answer 25

I've been trying to do f(x)=x(2x-5)^3 where u=2x-5 and y=x*u^3

Answer 26

I can't figure out why that doesn't work or where I go wrong. Yes, it's a longer route. I'm afraid this is the way she wants us to go on the test.

Answer 27

Am I choosing the wrong values for my inner/outer function or is it because there are actually three functions?

Answer 28

I think you'd be better off just differentiating the given function in the usual way. Then, if you wish, we could try doing it using a substitution.

If you insist on using a substitution first:

y=u*v

y ' = u*v ' + v*u '

where u=x, u ' = 1, v = (2x+5)^3 and v ' = 3(2x+5)^2*2= ??

Substitute these four components into the derivative equation, above.

Answer 29

I agree that Arqum's way was so much easier. I won't argue that!

Answer 30

yeah...

Answer 31

u're over complicating things here...just tell your professor to teach you guys the easy way not to confuse ya'll

Answer 32

Haha. She's not the type of professor you say that to =)

Answer 33

She's so confusing at times (and our textbook is worthless) that I went as far as to get the echapter for another textbook that covers this.

Answer 34

LOL... i know your feel bro.. ( u r a bro eh?)

Answer 35

As recommended to me by another professor in the math study hall.

Answer 36

No, a chick =P It's cool, though.

Answer 37

I appreciate everyone's help. Thank you.

Answer 38

No problem...