What is the derivative of sqrt(e^x+2) ?

The derivative of sqrt(e^x+2) is (e^x)/(2sqrt(e^x+2))

What is the first derivative of sqrt(e^x+2) ?

The first derivative of sqrt(e^x+2) is (e^x)/(2sqrt(e^x+2))

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

\frac{e ^{x}}{2 e ^{x} + 2}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{e ^{x}}{2 e ^{x} + 2}

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

\int \frac{x ^{3}}{( x ^{2} + 12 ) ^{3}} d x

\frac{d y}{d x} = \frac{1}{x ^{2} y ^{2}}

x^{2} e^{4 x}

\frac{d y}{d x} = e^{- ka \cdot x}, y (0) = 0

What is the derivative of sqrt(e^x+2) ?
The derivative of sqrt(e^x+2) is (e^x)/(2sqrt(e^x+2))
What is the first derivative of sqrt(e^x+2) ?
The first derivative of sqrt(e^x+2) is (e^x)/(2sqrt(e^x+2))