What is (\partial)/(\partial y)(ycos(yz)) ?

The answer to (\partial)/(\partial y)(ycos(yz)) is cos(yz)-yzsin(yz)

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(\partial)/(\partial y)(ycos(yz))

\frac{\partial}{\partial y} (y cos (yz))

cos (yz) - yz sin (yz)

Solution steps

\frac{\partial}{\partial y} (y cos (yz))

Treat

z

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = cos (yz)

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

\frac{\partial}{\partial y} (y) = 1

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

= 1 \cdot cos (yz) + (- sin (yz) z) y

Simplify

= cos (yz) - yz sin (yz)

\frac{d}{d x} (x^{3} + 3 x^{2} - 2)

y^{^{'}} = (1 + x) (1 + y)

x \to 0 lim (\frac{( 5 e ^{x} - 5 )}{x})

\frac{\partial}{\partial y} (x^{2} - 3 y^{2} + 7)

\int \frac{( x + 1 )}{( x - 1 )} d x

What is (\partial)/(\partial y)(ycos(yz)) ?
The answer to (\partial)/(\partial y)(ycos(yz)) is cos(yz)-yzsin(yz)