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Popular >

derivative of 540(1-e^{-0.1x})

Solution

\frac{d}{d x} (540 (1 - e^{- 0.1 x}))

Solution

54 e^{- 0.1 x}

Solution steps

\frac{d}{d x} (540 (1 - e^{- 0.1 x}))

Take the constant out:

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

= 540 \frac{d}{d x} (1 - e^{- 0.1 x})

Apply the Sum/Difference Rule:

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

= 540 (\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}

= 540 (0 - (- 0.1 e^{- 0.1 x}))

Simplify

= 54 e^{- 0.1 x}

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Frequently Asked Questions (FAQ)

What is the derivative of 540(1-e^{-0.1x}) ?
The derivative of 540(1-e^{-0.1x}) is 54e^{-0.1x}
What is the first derivative of 540(1-e^{-0.1x}) ?
The first derivative of 540(1-e^{-0.1x}) is 54e^{-0.1x}