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# Prove the following.. watch

1. erm,

d/dx ln | sinx | = cot x

2. Chain rule?
3. yeah, but will u go through it? I know u guys aren't meant to tell us the answers but if i can do this 1..then i will be able to do the rest, hopefully. cheers
4. aah got it..i was getting confused with integrastion.
5. (Original post by FoOtYdUdE)
erm,

d/dx ln | sinx | = cot x

Let's break this up shall we?

Let's find and :

and

And now to find you multiply them together.
6. OK If you differentiate ln (x ) wrt x you get 1/x
If you differentiate sin (x) wrt x you get cos x

You have to differentiate a function-of-a-function. First take x, then sin() it. Then ln() the result.

You start on the outside function - ln. And differentiate that. So 1/sin(x).

Then you go inside one layer. You find sin(x). So you differentiate that. cos(x). So we've written 1/sin(x) times cos(x).

Now we've only got x inside the sin, so we can stop.

Then cos(x)/sin(x) = cot(x) like 1/tan.

So to differentiate (yourgranny(x))^2 is just 2.yourgranny(x).d/dx(yourgranny(x))
7. The other way to do it is:
d/dx ln(f(x)) = f'(x)/f(x)
if that notation makes any sense.

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