What is the derivative of e^{-t}cos(pix) ?

The derivative of e^{-t}cos(pix) is -pie^{-t}sin(pix)

What is the first derivative of e^{-t}cos(pix) ?

The first derivative of e^{-t}cos(pix) is -pie^{-t}sin(pix)

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\frac{d}{d x} (e^{- t} cos (π x))

- π e^{- t} sin (π x)

Solution steps

\frac{d}{d x} (e^{- t} cos (π x))

Treat

t

as a constant

Take the constant out:

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

= e^{- t} \frac{d}{d x} (cos (π x))

Apply the chain rule:

- sin (π x) \frac{d}{d x} (π x)

= - sin (π x) \frac{d}{d x} (π x)

\frac{d}{d x} (π x) = π

= e^{- t} (- sin (π x) π)

Simplify

= - π e^{- t} sin (π x)

What is the derivative of e^{-t}cos(pix) ?
The derivative of e^{-t}cos(pix) is -pie^{-t}sin(pix)
What is the first derivative of e^{-t}cos(pix) ?
The first derivative of e^{-t}cos(pix) is -pie^{-t}sin(pix)