What is (\partial)/(\partial x)(e^{-2y}cos(pix)) ?

The answer to (\partial)/(\partial x)(e^{-2y}cos(pix)) is -pie^{-2y}sin(pix)

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(\partial)/(\partial x)(e^{-2y}cos(pix))

\frac{\partial}{\partial x} (e^{- 2 y} cos (π x))

- π e^{- 2 y} sin (π x)

Solution steps

\frac{\partial}{\partial x} (e^{- 2 y} cos (π x))

Treat

y

as a constant

Take the constant out:

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

= e^{- 2 y} \frac{\partial}{\partial x} (cos (π x))

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (π x) = π

= e^{- 2 y} (- sin (π x) π)

Simplify

= - π e^{- 2 y} sin (π x)

\int_{- 2}^{4} (x - 9) d x

\int \frac{x ^{3} + 25}{x ^{2} + 25} d x

x \to 2 lim (\frac{2}{x + 2})

\frac{d}{d x} (\frac{2 x}{5})

y^{^{'}} = \frac{( x ^{2} - y ^{2} )}{x y}, y (2) = 5

What is (\partial)/(\partial x)(e^{-2y}cos(pix)) ?
The answer to (\partial)/(\partial x)(e^{-2y}cos(pix)) is -pie^{-2y}sin(pix)