# Thread: Differentiation Question

1. ## Differentiation Question

Differentiate lnx/x^5

Using the quotient rule I got a final answer of x^4-lnx5x^4/x^10

First of all is this correct, if so is it in its simplest form.

Please help, thanks.

2. Originally Posted by haku
Differentiate lnx/x^5

Using the quotient rule I got a final answer of x^4-lnx5x^4/x^10

First of all is this correct, if so is it in its simplest form.

Please help, thanks.
it is correct, but it is not the simplest form. factor out the x^4 in the numerator and then cancel it into the denominator.

by the way, learn to use parentheses. you should have typed: (x^4 - 5x^4 * lnx)/(x^10)

3. Thanks for that help. Sorry for not using parenthesis. I now realise what I typed makes no sense!

4. For this example here:

(x^4 + 3)^3 cos2x

When differentiating would you use a combination of the chain rule and the product rule, giving an answer of:
(12x^2(x^4+3)^2(cos2x)) + ((x^4+3)^3(sin2x)).

Does this look okay?

5. Originally Posted by haku
For this example here:

(x^4 + 3)^3 cos2x

When differentiating would you use a combination of the chain rule and the product rule, giving an answer of:
(12x^2(x^4+3)^2(cos2x)) + ((x^4+3)^3(sin2x)).

Does this look okay?
that's not correct

6. Could you please help me get on the right track then?

7. Originally Posted by haku
Could you please help me get on the right track then?
recall that by the product rule we have that $\displaystyle \frac d{dx}f(x)g(x) = f'(x)g(x) + f(x)g'(x)$

here we have $\displaystyle f(x) = \left( x^4 + 3 \right)^3 \implies f'(x) = 12x^3 \left( x^4 + 3 \right)^2$ by the chain rule

and $\displaystyle g(x) = \cos 2x \implies g'(x) = -2 \sin 2x$ also by the chain rule

now just put the pieces together. with practice you will be able to do all this in one line without splitting up the parts like this, so keep at it

8. Thanks again for your help.