What is (\partial)/(\partial x)(x^2+e^{xy}) ?

The answer to (\partial)/(\partial x)(x^2+e^{xy}) is 2x+e^{xy}y

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(\partial)/(\partial x)(x^2+e^{xy})

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

2 x + e^{x y} y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x + e^{x y} y

\int 6 x^{8} (x^{9} + 3)^{5} d x

\int \frac{e ^{4 x}}{e ^{4 x} + 5} d x

\int \frac{e ^{x}}{8 + e ^{x}} d x

y = (4 x - e^{3 x})^{9}

y = x^{2}, (0, 1)

What is (\partial)/(\partial x)(x^2+e^{xy}) ?
The answer to (\partial)/(\partial x)(x^2+e^{xy}) is 2x+e^{xy}y