What is (\partial)/(\partial y)(e^xcos(piy)) ?

The answer to (\partial)/(\partial y)(e^xcos(piy)) is -pie^xsin(piy)

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(\partial)/(\partial y)(e^xcos(piy))

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

- π e^{x} sin (π y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= e^{x} \frac{\partial}{\partial y} (cos (π y))

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (π y) = π

= e^{x} (- sin (π y) π)

Simplify

= - π e^{x} sin (π y)

What is (\partial)/(\partial y)(e^xcos(piy)) ?
The answer to (\partial)/(\partial y)(e^xcos(piy)) is -pie^xsin(piy)