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

The answer to (\partial)/(\partial y)(cos(xy)+sin(yz)) is -sin(xy)x+cos(yz)z

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

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

- sin (x y) x + cos (yz) z

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (cos (x y)) = - sin (x y) x

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

= - sin (x y) x + cos (yz) z

\int \frac{7}{x ^{3}} d x

\frac{d}{d x} (\frac{2 x ln ( x ) + x ^{2} - 1}{x - 1})

\int_{1}^{e^{3}} \frac{ln ^{5} ( x ^{2} )}{x} d x

d er i v a t i v e 35 cos (x)

\frac{d}{d t} (\frac{1 - t ^{2}}{1 + t ^{2}})

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