# Thread: Partial Derivative of Transcendental Function

1. ## Partial Derivative of Transcendental Function

"Find the partial derivative of (sin(4x))^cos(3y) with respect to x and then with respect to y."

This one is pretty confusing. I've been doing partial derivatives with polynomials with ease up to this point, I can't find a solid example of this kind of problem though. Any tips or help is greatly, greatly appreciated. Thank you!

2. ## Re: Partial Derivative of Transcendental Function

Originally Posted by bobsanchez
"Find the partial derivative of (sin(4x))^cos(3y) with respect to x and then with respect to y."

This one is pretty confusing. I've been doing partial derivatives with polynomials with ease up to this point, I can't find a solid example of this kind of problem though. Any tips or help is greatly, greatly appreciated. Thank you!
${\frac {\partial }{\partial x}} \left( \left( \sin \left( 4\,x\right) \right) ^{\cos \left( 3\,y \right) } \right)=4\, \left( \sin \left( 4\,x \right) \right) ^{\cos \left( 3\,y\right) -1}\cos \left( 3\,y \right) \cos \left( 4\,x \right)$

${\frac {\partial }{\partial y}} \left( \left( \sin \left( 4\,x\right) \right) ^{\cos \left( 3\,y \right) } \right)=-3\, \left( \sin \left( 4\,x \right) \right) ^{\cos \left( 3\,y\right) }\sin \left( 3\,y \right) \ln \left( \sin \left( 4\,x\right) \right)$