What is the derivative of e^{sqrt(2x)}(sqrt(2x)-1) ?

The derivative of e^{sqrt(2x)}(sqrt(2x)-1) is e^{sqrt(2)sqrt(x)}

What is the first derivative of e^{sqrt(2x)}(sqrt(2x)-1) ?

The first derivative of e^{sqrt(2x)}(sqrt(2x)-1) is e^{sqrt(2)sqrt(x)}

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\frac{d}{d x} (e^{2 x} (2 x - 1))

e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} (2 x - 1))

Simplify

e^{2 x} (2 x - 1) : e^{2 x} (2 x - 1)

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

Apply the Product Rule:

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

f = e^{2 x}, g = 2 x - 1

= \frac{d}{d x} (e^{2 x}) (2 x - 1) + \frac{d}{d x} (2 x - 1) e^{2 x}

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

\frac{d}{d x} (2 x - 1) = \frac{1}{2 x}

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

Simplify

\frac{e ^{2 x}}{2 x} (2 x - 1) + \frac{1}{2 x} e^{2 x} : e^{2 x}

= e^{2 x}

What is the derivative of e^{sqrt(2x)}(sqrt(2x)-1) ?
The derivative of e^{sqrt(2x)}(sqrt(2x)-1) is e^{sqrt(2)sqrt(x)}
What is the first derivative of e^{sqrt(2x)}(sqrt(2x)-1) ?
The first derivative of e^{sqrt(2x)}(sqrt(2x)-1) is e^{sqrt(2)sqrt(x)}