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

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

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(\partial)/(\partial x)(2y+ye^x)

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

e^{x} y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + y e^{x}

Simplify

= e^{x} y

\frac{d x}{d t} = - 3 x

h \to 0 lim (\frac{e ^{2 h} - 1}{h})

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

f (x) = 2 x 5 - 2 x, at x = - 1

\int r d r

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