What is (\partial)/(\partial x)(cos(pixy)) ?

The answer to (\partial)/(\partial x)(cos(pixy)) is -sin(pixy)piy

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(\partial)/(\partial x)(cos(pixy))

\frac{\partial}{\partial x} (cos (π x y))

- sin (π x y) π y

Solution steps

\frac{\partial}{\partial x} (cos (π x y))

Treat

y

as a constant

Apply the chain rule:

- sin (π x y) \frac{\partial}{\partial x} (π x y)

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

\frac{\partial}{\partial x} (π x y) = π y

= - sin (π x y) π y

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What is (\partial)/(\partial x)(cos(pixy)) ?
The answer to (\partial)/(\partial x)(cos(pixy)) is -sin(pixy)piy