What is (\partial)/(\partial x)(e^{-5t}cos(pix)) ?

The answer to (\partial)/(\partial x)(e^{-5t}cos(pix)) is -pie^{-5t}sin(pix)

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(\partial)/(\partial x)(e^{-5t}cos(pix))

\frac{\partial}{\partial x} (e^{- 5 t} cos (π x))

- π e^{- 5 t} sin (π x)

Solution steps

\frac{\partial}{\partial x} (e^{- 5 t} cos (π x))

Treat

t

as a constant

Take the constant out:

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

= e^{- 5 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^{- 5 t} (- sin (π x) π)

Simplify

= - π e^{- 5 t} sin (π x)

What is (\partial)/(\partial x)(e^{-5t}cos(pix)) ?
The answer to (\partial)/(\partial x)(e^{-5t}cos(pix)) is -pie^{-5t}sin(pix)