# Math Help - differnentiation problem

1. ## differnentiation problem

Hello, I am trying to differentiate this:
x^3cos(lnx)

Would I be correct in using the chain rule like this? :

3x^2(cos(lnx) * -sin(lnx) * 1/x)

Thanks for any help.

2. You need to apply the product rule as well. You can't just differentiate each term in the product individually.

3. Also, you haven't correctly applied the chain rule. The derivative of cos(lnx) should just be -sin(lnx) * (1/x).

4. thanks for helping.
I have had another go at it.

Would I be right in saying the answer is:

3x^2cos(lnx) + x^3-sin(lnx) * 1/2

5. Originally Posted by fran1942
thanks for helping.
I have had another go at it.

Would I be right in saying the answer is:

3x^2cos(lnx) + x^3-sin(lnx) * 1/2
Your first term is correct, the second is wrong. This problem involves a product rule with a chain rule.

$\displaystyle\frac{d}{dx}x^3 cos(ln(x))=cos(ln(x))*3x^2 + x^3 \frac{d}{dx}(cos(ln(x))$

$=3x^2 cos(ln(x))-x^2sin(ln(x))$