What is (\partial)/(\partial x)(e^{-8t}cos(pix)) ?

The answer to (\partial)/(\partial x)(e^{-8t}cos(pix)) is -pie^{-8t}sin(pix)

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(\partial)/(\partial x)(e^{-8t}cos(pix))

\frac{\partial}{\partial x} (e^{- 8 t} cos (π x))

- π e^{- 8 t} sin (π x)

Solution steps

\frac{\partial}{\partial x} (e^{- 8 t} cos (π x))

Treat

t

as a constant

Take the constant out:

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

= e^{- 8 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^{- 8 t} (- sin (π x) π)

Simplify

= - π e^{- 8 t} sin (π x)

- x + 5, x^{2}

3 y d x + (x - x y) d y = 0

f (x) = \frac{10}{x}

y^{^{'}} + \frac{1}{t} y = 3 t

\int - 0.01 (1024 π)^{2} cos (1024 π) x d x

What is (\partial)/(\partial x)(e^{-8t}cos(pix)) ?
The answer to (\partial)/(\partial x)(e^{-8t}cos(pix)) is -pie^{-8t}sin(pix)