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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = x + 2 y

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

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

\frac{\partial}{\partial x} (x + 2 y) = 1

= e^{x} (x + 2 y) + 1 \cdot e^{x}

Simplify

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

\frac{\partial}{\partial y} (x^{2} - 6 y)

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (1) = 0, y^{^{'}} (1) = 1

\int \frac{3 + u}{u ^{2} - 1} d u

y = ln (x^{2} - 8 x + 1), (8, 0)

\frac{d}{d x} (5^{3 x^{3}})

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