y= e^sin 2x

Solution attempt:

lny = sin 2x

lny = 2sinxcosx

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- Mar 1st 2011, 07:13 PMFoxlionnatural differentiation
y= e^sin 2x

Solution attempt:

lny = sin 2x

lny = 2sinxcosx - Mar 1st 2011, 07:18 PMNOX Andrew

For , let . Then, .

Now, it is only a matter of substituting the values of and into the first equation at the top.

- Mar 1st 2011, 07:26 PMintegral

implicite differentiation.

chain rule

- Mar 1st 2011, 08:00 PMFoxlion
Then, .

Both of you have the correct answer, I get the use of the chain rule and it looks very clean but could you also use the product rule for ?

Thus making

did I just make a mistake? - Mar 1st 2011, 08:09 PMintegral
Product rule applies when you have the form: . (which you don't have here)

I am not sure where you are geting 2sin(2x)+2cos(2x) but if you will notice, the form of f(x) needing to use the chain rule is:

where p(x)=sin(x) and q(x)=2x - Mar 1st 2011, 08:12 PMFoxlion
Thank you integral, was confused as to which was the inside/ outside function. In fact I am rather ignorant of the transcendental functions altogether as I looked at sin2x as the product of sin and 2x.