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

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

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

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

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

e^{- x}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= - e^{- x} (- 1)

Simplify

= e^{- x}

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 8

\int c e^{- x} d x

\int \frac{sin ( 7 e ^{- 5 x} )}{e ^{5 x}} d x

\int \frac{x ^{2}}{x ^{2} - 9} d x

y^{^{'}} = y (3 - y) - \frac{9}{4}

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