What is (\partial)/(\partial x)(xcos(y)+ye^x) ?

The answer to (\partial)/(\partial x)(xcos(y)+ye^x) is cos(y)+ye^x

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(\partial)/(\partial x)(xcos(y)+ye^x)

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

cos (y) + y e^{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

e^{\frac{2}{3}}

\int_{- \frac{π}{4}}^{\frac{π}{4}} 1

\frac{d}{d x} (A (2 e^{- x} x - e^{- x} x^{2}))

\int_{1}^{e^{3}} x^{2} ln (x) d x

x \to 5 lim (123)

What is (\partial)/(\partial x)(xcos(y)+ye^x) ?
The answer to (\partial)/(\partial x)(xcos(y)+ye^x) is cos(y)+ye^x