Differentiation Question (Showing first derivative of something) (1 Viewer)

[TearsOfFire]

I'm stuck with this differentiation question:

Given y= x(x+1)^3, Show that dy/dx = (4x+1)(x+1)^2

So far, this is what I've done ( I'm not too sure if I'm correct)

You use the product rule and the chain rule, and I got

u=x, u'=1
v=(x+1)^3, v'=3(1)(x+1)^2 (You use the chain rule right?)

u'v + v'u


But then I get stuck... after subbing in the values I don't know how to get to show it.. Have I done something wrong?

Any help would be very much appreciated. I've just got a whole bunch of similar questions, but I'm able to differentiate but I have no idea how to work it out from there.

Thanks in advance

 

[independantz]

 

[Timothy.Siu]

lol

 

[lolokay]

so you have
(x+1)³ + 3(x+1)²x
..then factorise

 

[kurt.physics]

I'm stuck with this differentiation question:

Given y= x(x+1)^3, Show that dy/dx = (4x+1)(x+1)^2

So far, this is what I've done ( I'm not too sure if I'm correct)

You use the product rule and the chain rule, and I got

u=x, u'=1
v=(x+1)^3, v'=3(1)(x+1)^2 (You use the chain rule right?)

u'v + v'u


But then I get stuck... after subbing in the values I don't know how to get to show it.. Have I done something wrong?

Any help would be very much appreciated. I've just got a whole bunch of similar questions, but I'm able to differentiate but I have no idea how to work it out from there.

Thanks in advance

Okay, so you have done everything right, you just need to factorise in order to simplify. You have






As you know



therefore





Which can be written



So we are just factorizing out of it.

 

[TearsOfFire]

lol

lol, silly me. I've only just been taught how to differentiate, so I was kind of looking for some way to get the answer... But I forgot the basics of algebra. lol

 

[Finx]

Would it be possible to expand and differentiate?

 

[Timothy.Siu]

yeah thats fine

 

[Trebla]

A less conventional method (if you hate using the product rule) is that you could note that:
x(x + 1)³ = ([x + 1] - 1)(x + 1)³
= (x + 1)⁴ - (x + 1)³

Then you easily differentiate without thinking about the product rule lol

 

[azureus88]

A less conventional method (if you hate using the product rule) is that you could note that:
x(x + 1)³ = ([x + 1] - 1)(x + 1)³
= (x + 1)⁴ - (x + 1)³

Then you easily differentiate without thinking about the product rule lol

lol nice