What is (\partial)/(\partial y)(sin(8x)cos(3y)) ?

The answer to (\partial)/(\partial y)(sin(8x)cos(3y)) is -3sin(8x)sin(3y)

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(\partial)/(\partial y)(sin(8x)cos(3y))

\frac{\partial}{\partial y} (sin (8 x) cos (3 y))

- 3 sin (8 x) sin (3 y)

Solution steps

\frac{\partial}{\partial y} (sin (8 x) cos (3 y))

Treat

x

as a constant

Take the constant out:

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

= sin (8 x) \frac{\partial}{\partial y} (cos (3 y))

Apply the chain rule:

- sin (3 y) \frac{\partial}{\partial y} (3 y)

= - sin (3 y) \frac{\partial}{\partial y} (3 y)

\frac{\partial}{\partial y} (3 y) = 3

= sin (8 x) (- sin (3 y) \cdot 3)

Simplify

= - 3 sin (8 x) sin (3 y)

What is (\partial)/(\partial y)(sin(8x)cos(3y)) ?
The answer to (\partial)/(\partial y)(sin(8x)cos(3y)) is -3sin(8x)sin(3y)