What is (\partial)/(\partial x)(1/2 e^{2x}) ?

The answer to (\partial)/(\partial x)(1/2 e^{2x}) is e^{2x}

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(\partial)/(\partial x)(1/2 e^{2x})

\frac{\partial}{\partial x} (\frac{1}{2} e^{2 x})

e^{2 x}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2} e^{2 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{\partial}{\partial x} (e^{2 x})

Apply the chain rule:

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

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

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

= \frac{1}{2} e^{2 x} \cdot 2

Simplify

\frac{1}{2} e^{2 x} \cdot 2 : e^{2 x}

= e^{2 x}

What is (\partial)/(\partial x)(1/2 e^{2x}) ?
The answer to (\partial)/(\partial x)(1/2 e^{2x}) is e^{2x}