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

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

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

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

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derivative of

e^{x + 1}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 21 e^{x} d x

\int_{1}^{3} \frac{4}{x ^{2}} d x

9 - 5 x

\frac{d y}{d t} = e^{- 2 t + 3 y}

(- 2, - 6), (1, 6)

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