What is the derivative of 5(1-e^{-2x}) ?

The derivative of 5(1-e^{-2x}) is 10e^{-2x}

What is the first derivative of 5(1-e^{-2x}) ?

The first derivative of 5(1-e^{-2x}) is 10e^{-2x}

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\frac{d}{d x} (5 (1 - e^{- 2 x}))

10 e^{- 2 x}

Solution steps

\frac{d}{d x} (5 (1 - e^{- 2 x}))

Take the constant out:

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

= 5 \frac{d}{d x} (1 - e^{- 2 x})

Apply the Sum/Difference Rule:

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

= 5 (\frac{d}{d x} (1) - \frac{d}{d x} (e^{- 2 x}))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (e^{- 2 x}) = - 2 e^{- 2 x}

= 5 (0 - (- 2 e^{- 2 x}))

Simplify

= 10 e^{- 2 x}

\frac{d}{d x} (x^{2} + y^{2} - 4)

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What is the derivative of 5(1-e^{-2x}) ?
The derivative of 5(1-e^{-2x}) is 10e^{-2x}
What is the first derivative of 5(1-e^{-2x}) ?
The first derivative of 5(1-e^{-2x}) is 10e^{-2x}