# help finding a derivative

• Dec 16th 2009, 06:44 PM
twostep08
help finding a derivative
i got a big final exam coming up tomorrow, and i feel like im in big trouble. this was on the practice exam, and i want to make sure i understand it (there will be more to come throughout the rest of the night , im sure)

find the derivative of
3x^(sin(x^2))

can someone walk me through that so i understand it; thanks a ton
• Dec 16th 2009, 07:20 PM
firebio
Quote:

Originally Posted by twostep08
i got a big final exam coming up tomorrow, and i feel like im in big trouble. this was on the practice exam, and i want to make sure i understand it (there will be more to come throughout the rest of the night , im sure)

find the derivative of
3x^(sin(x^2))

can someone walk me through that so i understand it; thanks a ton

You can change the equation in terms to natural log.
So lny=sinx^2 ln3x?
then just differentiate it normally, so y'=y(dy/dx(sinx^2 ln3x))
• Dec 16th 2009, 07:30 PM
twostep08
ok..im very close to the answer i think...i got the right hand side to be what it should be...however im missing the 3x^sin(x^2) factor..

would i be right in using implicit differentiation to finish it off? i mean if i use the log approach, i would get 1/y * y' on the left. then multiply both sides by y, and plug in what we know y equals, because that is the answer to the problem. i just dont know if im taking any lberties i shouldnt be
• Dec 16th 2009, 07:31 PM
twostep08
nevermind, i think i understand your notation to mean that im right