What is the derivative of 5e^{-0.5x}+100 ?

The derivative of 5e^{-0.5x}+100 is -2.5e^{-0.5x}

What is the first derivative of 5e^{-0.5x}+100 ?

The first derivative of 5e^{-0.5x}+100 is -2.5e^{-0.5x}

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\frac{d}{d x} (5 e^{- 0.5 x} + 100)

- 2.5 e^{- 0.5 x}

Solution steps

\frac{d}{d x} (5 e^{- 0.5 x} + 100)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 e^{- 0.5 x}) + \frac{d}{d x} (100)

\frac{d}{d x} (5 e^{- 0.5 x}) = - 2.5 e^{- 0.5 x}

\frac{d}{d x} (100) = 0

= - 2.5 e^{- 0.5 x} + 0

Simplify

= - 2.5 e^{- 0.5 x}

What is the derivative of 5e^{-0.5x}+100 ?
The derivative of 5e^{-0.5x}+100 is -2.5e^{-0.5x}
What is the first derivative of 5e^{-0.5x}+100 ?
The first derivative of 5e^{-0.5x}+100 is -2.5e^{-0.5x}