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Popular >

derivative of e^{3x}+e^{x+e^{-2x}}

Solution

\frac{d}{d x} (e^{3 x} + e^{x + e^{- 2 x}})

Solution

e^{3 x} \cdot 3 + e^{x + e^{- 2 x}} (1 - 2 e^{- 2 x})

Solution steps

\frac{d}{d x} (e^{3 x} + e^{x + e^{- 2 x}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{3 x}) + \frac{d}{d x} (e^{x + e^{- 2 x}})

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

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

= e^{3 x} \cdot 3 + e^{x + e^{- 2 x}} (1 - 2 e^{- 2 x})

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Frequently Asked Questions (FAQ)

What is the derivative of e^{3x}+e^{x+e^{-2x}} ?
The derivative of e^{3x}+e^{x+e^{-2x}} is e^{3x}*3+e^{x+e^{-2x}}(1-2e^{-2x})
What is the first derivative of e^{3x}+e^{x+e^{-2x}} ?
The first derivative of e^{3x}+e^{x+e^{-2x}} is e^{3x}*3+e^{x+e^{-2x}}(1-2e^{-2x})