Question #345472

Suppose z is a function of x and y and tan(√x + y) = e^z^2. Determine ∂z/∂x and ∂z/∂y.

1
Expert's answer
2022-05-30T02:28:51-0400
tan(x+y)=ez2\tan(\sqrt{x}+y)=e^{z^2}

Differentiate both sides with respect to xx


1cos2(x+y)(12x)=2zez2zx\dfrac{1}{\cos ^2(\sqrt{x}+y)}(\dfrac{1}{2\sqrt{x}})=2ze^{z^2}\dfrac{\partial z}{\partial x}

zx=14zez2xcos2(x+y)\dfrac{\partial z}{\partial x}=\dfrac{1}{4ze^{z^2}\sqrt{x}\cos ^2(\sqrt{x}+y)}



tan(x+y)=ez2\tan(\sqrt{x}+y)=e^{z^2}

Differentiate both sides with respect to yy

1cos2(x+y)(1)=2zez2zy\dfrac{1}{\cos ^2(\sqrt{x}+y)}(1)=2ze^{z^2}\dfrac{\partial z}{\partial y}

zy=12zez2cos2(x+y)\dfrac{\partial z}{\partial y}=\dfrac{1}{2ze^{z^2}\cos ^2(\sqrt{x}+y)}




Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS