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

The answer to (\partial)/(\partial x)(1+e^{-xy}cos(y)) is -e^{-xy}ycos(y)

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(\partial)/(\partial x)(1+e^{-xy}cos(y))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (1) + \frac{\partial}{\partial x} (e^{- x y} cos (y))

\frac{\partial}{\partial x} (1) = 0

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

= 0 - y e^{- y x} cos (y)

Simplify

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

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\int_{2}^{3} \frac{1}{x} d x

What is (\partial)/(\partial x)(1+e^{-xy}cos(y)) ?
The answer to (\partial)/(\partial x)(1+e^{-xy}cos(y)) is -e^{-xy}ycos(y)