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

The answer to (\partial)/(\partial x)(e^xcos(y)+x) is cos(y)e^x+1

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

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

cos (y) e^{x} + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= cos (y) e^{x} + 1

\frac{\partial}{\partial x} (8 y - x^{4} sin (x y))

\frac{d}{d x} (- 6 x + 1)

\frac{\partial}{\partial x} (z sin (x y^{2} + 2 z))

\frac{\partial}{\partial x} (x y + z^{3} x - 2 yz)

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

What is (\partial)/(\partial x)(e^xcos(y)+x) ?
The answer to (\partial)/(\partial x)(e^xcos(y)+x) is cos(y)e^x+1