What is (\partial)/(\partial x)(e^xcos(y)+2x-3y^2) ?

The answer to (\partial)/(\partial x)(e^xcos(y)+2x-3y^2) is e^xcos(y)+2

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(\partial)/(\partial x)(e^xcos(y)+2x-3y^2)

\frac{\partial}{\partial x} (e^{x} cos (y) + 2 x - 3 y^{2})

e^{x} cos (y) + 2

Solution steps

\frac{\partial}{\partial x} (e^{x} cos (y) + 2 x - 3 y^{2})

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

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

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (3 y^{2}) = 0

= cos (y) e^{x} + 2 - 0

Simplify

= e^{x} cos (y) + 2

2 + t + \frac{1}{t}

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

\frac{d}{d x} (\frac{cosh ( x )}{sin ^{2} ( x )})

\frac{d}{d x} (5 cos (5 x))

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

What is (\partial)/(\partial x)(e^xcos(y)+2x-3y^2) ?
The answer to (\partial)/(\partial x)(e^xcos(y)+2x-3y^2) is e^xcos(y)+2