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

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

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

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

- π e^{- 2 t} sin (π x)

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

= e^{- 2 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^{- 2 t} (- sin (π x) π)

Simplify

= - π e^{- 2 t} sin (π x)

\frac{d y}{d t} = \frac{t}{y e ^{y + t^{2}}}

\int \frac{x ^{2}}{a ^{2} + ( x - b ) ^{2}} d x

\int 5 x cos (8 x) d x

d er i v a t i v e f (x) = x^{3} (x - 4)^{2}

\frac{d}{d x} (- 2 x (e^{- 2 x}))

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