What is (\partial)/(\partial x)(e^{-1}cos(pix)) ?

The answer to (\partial)/(\partial x)(e^{-1}cos(pix)) is -pi/e sin(pix)

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(\partial)/(\partial x)(e^{-1}cos(pix))

\frac{\partial}{\partial x} (e^{- 1} cos (π x))

- \frac{π}{e} sin (π x)

Solution steps

\frac{\partial}{\partial x} (e^{- 1} cos (π x))

Take the constant out:

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

= e^{- 1} \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^{- 1} (- sin (π x) π)

Simplify

e^{- 1} (- sin (π x) π) : - \frac{π}{e} sin (π x)

= - \frac{π}{e} sin (π x)

What is (\partial)/(\partial x)(e^{-1}cos(pix)) ?
The answer to (\partial)/(\partial x)(e^{-1}cos(pix)) is -pi/e sin(pix)