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}

(3 x + 2 3 x)^{^{'}}

f (x) = 3 x^{3} - 3 x, (- 1, 0)

\frac{\partial}{\partial u} (4 - u^{2} - v^{2})

\int - 2 x - 1 d x

x \to \infty lim (0 \cdot x)

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