What is (\partial)/(\partial x)(cos(8x)sin(4y)) ?

The answer to (\partial)/(\partial x)(cos(8x)sin(4y)) is -8sin(8x)sin(4y)

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(\partial)/(\partial x)(cos(8x)sin(4y))

\frac{\partial}{\partial x} (cos (8 x) sin (4 y))

- 8 sin (8 x) sin (4 y)

Solution steps

\frac{\partial}{\partial x} (cos (8 x) sin (4 y))

Treat

y

as a constant

Take the constant out:

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

= sin (4 y) \frac{\partial}{\partial x} (cos (8 x))

Apply the chain rule:

- sin (8 x) \frac{\partial}{\partial x} (8 x)

= - sin (8 x) \frac{\partial}{\partial x} (8 x)

\frac{\partial}{\partial x} (8 x) = 8

= sin (4 y) (- sin (8 x) \cdot 8)

Simplify

= - 8 sin (8 x) sin (4 y)

What is (\partial)/(\partial x)(cos(8x)sin(4y)) ?
The answer to (\partial)/(\partial x)(cos(8x)sin(4y)) is -8sin(8x)sin(4y)