What is (\partial)/(\partial x)(xe^y+x^2cos(y)) ?

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

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(\partial)/(\partial x)(xe^y+x^2cos(y))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\int e^{1.25 x} d x

\frac{21 x ^{2} + 6 x - 6}{2 x x}

\int \frac{1}{9 x ^{2} - 25} d x

\int \frac{1}{x + 1 + x - 1} d x

f (x) = x^{2} - 1, g (x) = - x + 2, 0, 1

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