What is (\partial)/(\partial y)(xsin(y)sin(z)) ?

The answer to (\partial)/(\partial y)(xsin(y)sin(z)) is xsin(z)cos(y)

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(\partial)/(\partial y)(xsin(y)sin(z))

\frac{\partial}{\partial y} (x sin (y) sin (z))

x sin (z) cos (y)

Solution steps

\frac{\partial}{\partial y} (x sin (y) sin (z))

Treat

x, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the common derivative:

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

= x sin (z) cos (y)

What is (\partial)/(\partial y)(xsin(y)sin(z)) ?
The answer to (\partial)/(\partial y)(xsin(y)sin(z)) is xsin(z)cos(y)