What is (\partial)/(\partial x)(ue^{2x}) ?

The answer to (\partial)/(\partial x)(ue^{2x}) is (\partial)/(\partial x)(u)e^{2x}+e^{2x}*2u

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(\partial)/(\partial x)(ue^{2x})

\frac{\partial}{\partial x} (u e^{2 x})

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

Solution steps

\frac{\partial}{\partial x} (u e^{2 x})

Apply the Product Rule:

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

f = u, g = e^{2 x}

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

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

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

\int \frac{- 8}{( x - 2 ) ( x ^{2} + 4 )} d x

- 3 y^{^{'}} + 9 x^{2} = 0

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

(x x)^{^{'}}

\frac{d y}{d t} + 7 y = e^{4 t}, y (0) = 10

What is (\partial)/(\partial x)(ue^{2x}) ?
The answer to (\partial)/(\partial x)(ue^{2x}) is (\partial)/(\partial x)(u)e^{2x}+e^{2x}*2u