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

The answer to (\partial)/(\partial x)(e^{-x}cos(piy)) is -e^{-x}cos(piy)

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

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

- e^{- x} cos (π y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

e^{- x} \frac{\partial}{\partial x} (- x)

= e^{- x} \frac{\partial}{\partial x} (- x)

\frac{\partial}{\partial x} (- x) = - 1

= cos (π y) e^{- x} (- 1)

Simplify

= - e^{- x} cos (π y)

\frac{1}{s - 1} \cdot e^{- s}

\frac{d}{d x} (\frac{350}{x ^{2} + y ^{2}})

(x^{3} e^{- 3 x})^{^{'}}

y = x^{2}

2 \frac{d y}{d x} + \frac{1}{x} y = x^{2} y^{- 1}

What is (\partial)/(\partial x)(e^{-x}cos(piy)) ?
The answer to (\partial)/(\partial x)(e^{-x}cos(piy)) is -e^{-x}cos(piy)