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

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

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

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

3 x^{2} + e^{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 3 x^{2} + e^{y} - 0

Simplify

= 3 x^{2} + e^{y}

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

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

\frac{d}{d x} (- e^{x} cos (x))

f (x) = 2 7 x + 1, at x = 9

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