find the derivative of : f(x)=2sin(e^x)ln(sqrt(x))

Question

anonymous · Answer

Eww, that's a gross derivative. Know how product rule and chain rule work?

anonymous · Answer

Yes I have the result I would just like someone to compute it to check against/ask why I got something different if that occurred.

anonymous · Answer

All right, give me a minute.

anonymous · Answer

kk ty

anonymous · Answer

2e^x*sin(e^x)*lnsqrt(x)+2sin(e^x)*1/x

anonymous · Answer

Sorry, that should be 1/(2x) at the end.

anonymous · Answer

Is that what you got?

anonymous · Answer

$$sine(e^x)/x + 2\cos(e^x)*e^x*\ln \sqrt{x}$$

is the correct answer

anonymous · Answer

I had forgotten to derive the sin, it's actually 2*e^x*cos(e^x)*ln(sqrt(x))+2*sin(e^x)*1/(2*x)

The answer that you had didn't use chain rule for ln(sqrt(x)), you just took the derivative of ln x.

anonymous · Answer

You do realize log(sqrt(x)) = 1/2log(x)? I simply did some algebra before integration. Nonetheless your 2nd result is the result I posted.

anonymous · Answer

Yeah, you're right.

anonymous · Answer

Thx for the response though sir.

anonymous · Answer

Not a problem.