What is the derivative of 7/(e^x) ?

The derivative of 7/(e^x) is -7e^{-x}

What is the first derivative of 7/(e^x) ?

The first derivative of 7/(e^x) is -7e^{-x}

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\frac{d}{d x} (\frac{7}{e ^{x}})

- 7 e^{- x}

Solution steps

\frac{d}{d x} (\frac{7}{e ^{x}})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{1}{e ^{x}})

Apply exponent rule:

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

= 7 \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

= 7 e^{- x} (- 1)

Simplify

= - 7 e^{- x}

What is the derivative of 7/(e^x) ?
The derivative of 7/(e^x) is -7e^{-x}
What is the first derivative of 7/(e^x) ?
The first derivative of 7/(e^x) is -7e^{-x}