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# C3 Differentiation problem watch

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1. how do you differentiate this??

y=ln(x^2cosx)

the answer is 2/x - tanx

i keep getting stuck!!
2. Make a substitution .

Use the product rule to find

Find

Then apply the chain rule.
3. Or you could just find the differential of x^2cosx using the product rule and then note that if

4. split it up. Using log rules you can simplify it a lot.
5. i've split it up and found it to be

1/x (-xsinx + 2cosx)

but i'm not sure how to go on from there
6. Using Dad's "splitting up" method, you should have obtained:

7. Nice method.
8. v(du/dx) + u(dv/dx)
9. (Original post by insparato)
Or you could just find the differential of x^2cosx using the product rule and then note that if

Yeah, we've just been told to know that. We were taught the chain rule for half a lesson but then the said the 'or otherwise' method, written in the exam questions is quicker and easier. So just do the above and you'll get the answer straight away
10. Being able to prove that result isn't really something that's required at A level. I'm sure its a result you can obtain through differentiation by first principles with a bit of limit knowledge and algebraic manipulation.

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Updated: November 15, 2008
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