What is the derivative of 100xe^{-0.5x} ?

The derivative of 100xe^{-0.5x} is 100(e^{-0.5x}-0.5e^{-0.5x}x)

What is the first derivative of 100xe^{-0.5x} ?

The first derivative of 100xe^{-0.5x} is 100(e^{-0.5x}-0.5e^{-0.5x}x)

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

100 (e^{- 0.5 x} - 0.5 e^{- 0.5 x} x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- 0.5 x}

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

\frac{d x}{d x} = 1

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

= 100 (1 \cdot e^{- 0.5 x} + (- 0.5 e^{- 0.5 x}) x)

Simplify

= 100 (e^{- 0.5 x} - 0.5 e^{- 0.5 x} x)

What is the derivative of 100xe^{-0.5x} ?
The derivative of 100xe^{-0.5x} is 100(e^{-0.5x}-0.5e^{-0.5x}x)
What is the first derivative of 100xe^{-0.5x} ?
The first derivative of 100xe^{-0.5x} is 100(e^{-0.5x}-0.5e^{-0.5x}x)