Edexcel C3 Differentiation help

I'm currently doing questions in the Pearson book and can't seem to find the answer for exercise 8B, question 1D.

The question is: Differentiate 3x^2(5x-1)^-1, this should be done from using the product rule.

Help would be greatly appreciated :smile:

Reply 1

mikeha

5

So you know you need the differential of 3x^2 multiplied by (5x-1)^-1 plus

3x^2 multiplied by differential of (5x-1)^-1.

So which part are you stuck on?

Reply 2

Farhan.Hanif93

18

Original post by monstercable

I'm currently doing questions in the Pearson book and can't seem to find the answer for exercise 8B, question 1D.

The question is: Differentiate 3x^2(5x-1)^-1, this should be done from using the product rule.

Help would be greatly appreciated :smile:

What have you tried? You need to show some working if you want help on here.

Reply 3

monstercable

OP

12

Well I've gotten as far as -15x^2(5x-1)^-2+6x(5x-1)^-1, but I don't know how to simplify this for the answer of 3x(5x-2)(5x-1)^-2

Reply 4

mikeha

5

Original post by monstercable

Well I've gotten as far as -15x^2(5x-1)^-2+6x(5x-1)^-1, but I don't know how to simplify this for the answer of 3x(5x-2)(5x-1)^-2

Well, you can see they are looking for a common denominator...........

You have two terms, one divided by the required denominator, the other not.

So for the term NOT divided by (5x-1) ^-2 what do you need to do to it to get it divided by that term?

Reply 5

mikeha

5

And when you've got that -- just add the two terms together, over the common denominator, and yo should find the numerator simplifies to the required expression (although I haven't checked it myself!)

Reply 6

monstercable

OP

12

Sorry, but I don't have a clue on how to do that :/

OP

any help?

\dfrac{a}{b} + \dfrac{c}{b^2} = \dfrac{ab+c}{b^2}

OP

That didn't work?

For those who still rely on these posts:

v = 3x^2 u = 1/(5x-1)

dv/dx = 6x du/dx = -5(5x-1)^-2
using the chain rule

dy/dx = udv/dx + vdu/dx

= [(1/(5x-1))6x]+ [3x^2(-5(5x-1)^-2)]

= 6x/(5x-1)^2 + [(-15x^2)/(5x-1)^2]

= [(30x^2-6x)/(5x-1)^2] + [(-15x^2)/(5x-1)^2]

= (15x^2-6x)/(5x-1)^2

= 3x(5x-2)/(5x-1)^2

= 3x(5x-2)(5x-1)^-2

These questions can easily cath you out.