What is (\partial)/(\partial x)(e^{-3y}cos(pix)) ?

The answer to (\partial)/(\partial x)(e^{-3y}cos(pix)) is -pie^{-3y}sin(pix)

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(\partial)/(\partial x)(e^{-3y}cos(pix))

\frac{\partial}{\partial x} (e^{- 3 y} cos (π x))

- π e^{- 3 y} sin (π x)

Solution steps

\frac{\partial}{\partial x} (e^{- 3 y} cos (π x))

Treat

y

as a constant

Take the constant out:

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

= e^{- 3 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^{- 3 y} (- sin (π x) π)

Simplify

= - π e^{- 3 y} sin (π x)

6 y^{^{''}} - y^{^{'}} - 2 y = 0

\int \frac{1 + sin ( x )}{1 + cos ( x )} d x

\frac{\partial}{\partial x} (\frac{( y - 3 x )}{z})

f (x) = x^{2} + 8, (- 3, 17)

\int_{2}^{7} \frac{1}{x ^{2} - 1} d x

What is (\partial)/(\partial x)(e^{-3y}cos(pix)) ?
The answer to (\partial)/(\partial x)(e^{-3y}cos(pix)) is -pie^{-3y}sin(pix)