# Math Help - 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.

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.

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

7. Originally Posted by haku
recall that by the product rule we have that $\frac d{dx}f(x)g(x) = f'(x)g(x) + f(x)g'(x)$
here we have $f(x) = \left( x^4 + 3 \right)^3 \implies f'(x) = 12x^3 \left( x^4 + 3 \right)^2$ by the chain rule
and $g(x) = \cos 2x \implies g'(x) = -2 \sin 2x$ also by the chain rule