What is the derivative of 0.0225xe^{-0.0467x} ?

The derivative of 0.0225xe^{-0.0467x} is 0.0225(e^{-0.0467x}-0.0467e^{-0.0467x}x)

What is the first derivative of 0.0225xe^{-0.0467x} ?

The first derivative of 0.0225xe^{-0.0467x} is 0.0225(e^{-0.0467x}-0.0467e^{-0.0467x}x)

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\frac{d}{d x} (0.0225 x e^{- 0.0467 x})

0.0225 (e^{- 0.0467 x} - 0.0467 e^{- 0.0467 x} x)

Solution steps

\frac{d}{d x} (0.0225 x e^{- 0.0467 x})

Take the constant out:

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

= 0.0225 \frac{d}{d x} (x e^{- 0.0467 x})

Apply the Product Rule:

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

f = x, g = e^{- 0.0467 x}

= 0.0225 (\frac{d x}{d x} e^{- 0.0467 x} + \frac{d}{d x} (e^{- 0.0467 x}) x)

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

\frac{d}{d x} (e^{- 0.0467 x}) = - 0.0467 e^{- 0.0467 x}

= 0.0225 (1 \cdot e^{- 0.0467 x} + (- 0.0467 e^{- 0.0467 x}) x)

Simplify

= 0.0225 (e^{- 0.0467 x} - 0.0467 e^{- 0.0467 x} x)

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What is the derivative of 0.0225xe^{-0.0467x} ?
The derivative of 0.0225xe^{-0.0467x} is 0.0225(e^{-0.0467x}-0.0467e^{-0.0467x}x)
What is the first derivative of 0.0225xe^{-0.0467x} ?
The first derivative of 0.0225xe^{-0.0467x} is 0.0225(e^{-0.0467x}-0.0467e^{-0.0467x}x)