What is the derivative of 1-e^{-0.1x} ?

The derivative of 1-e^{-0.1x} is 0.1e^{-0.1x}

What is the first derivative of 1-e^{-0.1x} ?

The first derivative of 1-e^{-0.1x} is 0.1e^{-0.1x}

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\frac{d}{d x} (1 - e^{- 0.1 x})

0.1 e^{- 0.1 x}

Solution steps

\frac{d}{d x} (1 - e^{- 0.1 x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) - \frac{d}{d x} (e^{- 0.1 x})

\frac{d}{d x} (1) = 0

\frac{d}{d x} (e^{- 0.1 x}) = - 0.1 e^{- 0.1 x}

= 0 - (- 0.1 e^{- 0.1 x})

Simplify

= 0.1 e^{- 0.1 x}

What is the derivative of 1-e^{-0.1x} ?
The derivative of 1-e^{-0.1x} is 0.1e^{-0.1x}
What is the first derivative of 1-e^{-0.1x} ?
The first derivative of 1-e^{-0.1x} is 0.1e^{-0.1x}