What is the derivative of 0.5e^{-0.5(x-1}) ?

The derivative of 0.5e^{-0.5(x-1}) is -0.25e^{-0.5(x-1)}

What is the first derivative of 0.5e^{-0.5(x-1}) ?

The first derivative of 0.5e^{-0.5(x-1}) is -0.25e^{-0.5(x-1)}

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\frac{d}{d x} (0.5 e^{- 0.5 (x - 1)})

- 0.25 e^{- 0.5 (x - 1)}

Solution steps

\frac{d}{d x} (0.5 e^{- 0.5 (x - 1)})

Take the constant out:

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

= 0.5 \frac{d}{d x} (e^{- 0.5 (x - 1)})

Apply the chain rule:

e^{- 0.5 (x - 1)} \frac{d}{d x} (- 0.5 (x - 1))

= e^{- 0.5 (x - 1)} \frac{d}{d x} (- 0.5 (x - 1))

\frac{d}{d x} (- 0.5 (x - 1)) = - 0.5

= 0.5 e^{- 0.5 (x - 1)} (- 0.5)

Simplify

= - 0.25 e^{- 0.5 (x - 1)}

What is the derivative of 0.5e^{-0.5(x-1}) ?
The derivative of 0.5e^{-0.5(x-1}) is -0.25e^{-0.5(x-1)}
What is the first derivative of 0.5e^{-0.5(x-1}) ?
The first derivative of 0.5e^{-0.5(x-1}) is -0.25e^{-0.5(x-1)}