What is (\partial)/(\partial z)(cos(xy)+sin(yz)) ?

The answer to (\partial)/(\partial z)(cos(xy)+sin(yz)) is ycos(yz)

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(\partial)/(\partial z)(cos(xy)+sin(yz))

\frac{\partial}{\partial z} (cos (x y) + sin (yz))

y cos (yz)

Solution steps

\frac{\partial}{\partial z} (cos (x y) + sin (yz))

Treat

x, y

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial z} (cos (x y)) + \frac{\partial}{\partial z} (sin (yz))

\frac{\partial}{\partial z} (cos (x y)) = 0

\frac{\partial}{\partial z} (sin (yz)) = cos (yz) y

= 0 + cos (yz) y

Simplify

= y cos (yz)

\int sin^{3} (x) cos^{2} (x) d x

\int_{1}^{e^{2}} \frac{ln ^{5} ( x ^{2} )}{x} d x

f (x) = (4 x - 5) (3 x^{3} - x^{2} + 1)

\int \frac{x - 3}{x ^{2} - 1} d x

x^{3}

What is (\partial)/(\partial z)(cos(xy)+sin(yz)) ?
The answer to (\partial)/(\partial z)(cos(xy)+sin(yz)) is ycos(yz)