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

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

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

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

- e^{- x y} y cos (y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= cos (y) e^{- x y} (- y)

Simplify

= - e^{- x y} y cos (y)

\frac{1}{s ^{2} ( s ^{2} + 3 s + 10 )}

\frac{d}{d x} (\frac{4 e ^{2 x} - 2 e ^{x} + 1}{2 e ^{2 x}})

\int 3 x^{2} e^{x} d x

\frac{\partial}{\partial x} (- 2 y csc^{3} (x))

\frac{d}{d x} (2 cos^{2} (x^{2} + 2))

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