What is (\partial)/(\partial x)(e^xx+e^x2y) ?

The answer to (\partial)/(\partial x)(e^xx+e^x2y) is e^xx+e^x+2ye^x

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(\partial)/(\partial x)(e^xx+e^x2y)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\int \frac{sin ( nπ x )}{nπ} d x

\frac{d y}{d x} = \frac{1}{x ^{2} + 1}

\frac{d}{d x} (- 2 x^{\frac{9}{8}})

x \to 30 lim (30)

\int_{0}^{1} \frac{8}{x ( x + 1 )} d x

What is (\partial)/(\partial x)(e^xx+e^x2y) ?
The answer to (\partial)/(\partial x)(e^xx+e^x2y) is e^xx+e^x+2ye^x