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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (- (\frac{1}{x} + 1)^{x})

y \to 0 lim (sin (3 y))

x \to 1 - lim (2 + x)

\frac{d}{d x} (\frac{\frac{d}{d x} ( 15 e ^{4 x} )}{8 x ^{2}})

\int 5 a^{2} x^{6} d x

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