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

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

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

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

- π e^{- t} sin (π x)

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

= e^{- t} \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^{- t} (- sin (π x) π)

Simplify

= - π e^{- t} sin (π x)

\int tan (2 x) sec^{2} (2 x) d x

\int \frac{e ^{t}}{e ^{2 t} + 3 e ^{t} + 2} d t

\int_{y}^{2} \frac{3}{16} x y d x

x^{2} + 21, at x = 2

x \to 1 lim (\frac{4 x - 4}{x - 1})

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