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Popular >

derivative of 20(e^{-x}-e^{-2x})

Solution

\frac{d}{d x} (20 (e^{- x} - e^{- 2 x}))

Solution

20 (- e^{- x} + 2 e^{- 2 x})

Solution steps

\frac{d}{d x} (20 (e^{- x} - e^{- 2 x}))

Take the constant out:

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

= 20 \frac{d}{d x} (e^{- x} - e^{- 2 x})

Apply the Sum/Difference Rule:

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

= 20 (\frac{d}{d x} (e^{- x}) - \frac{d}{d x} (e^{- 2 x}))

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

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

= 20 (- e^{- x} - (- 2 e^{- 2 x}))

Simplify

= 20 (- e^{- x} + 2 e^{- 2 x})

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Frequently Asked Questions (FAQ)

What is the derivative of 20(e^{-x}-e^{-2x}) ?
The derivative of 20(e^{-x}-e^{-2x}) is 20(-e^{-x}+2e^{-2x})
What is the first derivative of 20(e^{-x}-e^{-2x}) ?
The first derivative of 20(e^{-x}-e^{-2x}) is 20(-e^{-x}+2e^{-2x})