What is the derivative of 1000(1-e^{-0.15x}) ?

The derivative of 1000(1-e^{-0.15x}) is 150e^{-0.15x}

What is the first derivative of 1000(1-e^{-0.15x}) ?

The first derivative of 1000(1-e^{-0.15x}) is 150e^{-0.15x}

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\frac{d}{d x} (1000 (1 - e^{- 0.15 x}))

150 e^{- 0.15 x}

Solution steps

\frac{d}{d x} (1000 (1 - e^{- 0.15 x}))

Take the constant out:

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

= 1000 \frac{d}{d x} (1 - e^{- 0.15 x})

Apply the Sum/Difference Rule:

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

= 1000 (\frac{d}{d x} (1) - \frac{d}{d x} (e^{- 0.15 x}))

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

\frac{d}{d x} (e^{- 0.15 x}) = - 0.15 e^{- 0.15 x}

= 1000 (0 - (- 0.15 e^{- 0.15 x}))

Simplify

= 150 e^{- 0.15 x}

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What is the derivative of 1000(1-e^{-0.15x}) ?
The derivative of 1000(1-e^{-0.15x}) is 150e^{-0.15x}
What is the first derivative of 1000(1-e^{-0.15x}) ?
The first derivative of 1000(1-e^{-0.15x}) is 150e^{-0.15x}