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

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

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

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

e^{x} x + e^{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x

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

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

\frac{\partial}{\partial x} (x) = 1

= e^{x} x + 1 \cdot e^{x}

Simplify

= e^{x} x + e^{x}

\frac{\partial}{\partial y} (- \frac{1}{y})

\frac{d y}{d t} = y (1 - 0.0002 y)

\int 2^{x} x d x

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (π) = 0, y^{^{'}} (π) = 2

f (x) = 3 x^{2}, at x = 4

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