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

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

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

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

- cos (8 y) cos (x)

Solution steps

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

Simplify

sin (- x) cos (8 y) : - sin (x) cos (8 y)

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= - cos (8 y) cos (x)

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