Find an expression for dy/dx

Question

lukecrayonz · Answer

writing it atm

lukecrayonz · Answer

$$y=\frac{ 7 }{ u^2 } ; u=6x-7 $$

lukecrayonz · Answer

So input 6x-7

7/(6x-7)^2

lukecrayonz · Answer

I'm not sure if I should chain rule the bottom?

wolfe8 · Answer

Are you familiar with deriving using substitution? What you are given is the start of that method. After replacing a term with u, you find the du/dx of it. Here is the part you should have done at the beginning of your answer:

Using the chain rule, d/dx(1/(6 x-7)^2) =  d/( du)1/u^2 ( du)/( dx), where u = 6 x-7 and ( d)/( du)(1/u^2) = -2/u^3:
  =  7 -(2 (d/dx(-7+6 x)))/(-7+6 x)^3

Can you understand it if I just write that?

lukecrayonz · Answer

Yes I understand.
Final answer:
-84/(6x-7)^3

wolfe8 · Answer

You might want to check your power.

lukecrayonz · Answer

I got it right :O

wolfe8 · Answer

Oh my bad. Yes that is right.

lukecrayonz · Answer

Differentiate:
1/sqrt(4x+7)

wolfe8 · Answer

You can rewrite that one into $$\left( 4x-7 \right)^{-1/2}$$Then it should be simple enough to differentiate normally.

lukecrayonz · Answer

That's what I thought, so it's basically quotient rule changed over to chain rule.

lukecrayonz · Answer

Well not really quotient rule but you know what I mean.

wolfe8 · Answer

Probably what you mean