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Popular >

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

Solution

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

Solution

e^{x} + e^{x + e^{- x}} (1 - e^{- x})

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x} + e^{x + e^{- x}} (1 - e^{- x})

Popular Examples

integral of 30(25-t^2)

\int 30 (25 - t^{2}) d t

derivative of x^3Inx

\frac{d}{d x} (x^{3} I n x)

(\partial)/(\partial x)(e^{2x+3y})

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integral from 0 to 5 of pi(x+1)^2

\int_{0}^{5} π (x + 1)^{2} d x

integral of (12x^4-5x^3-7)

\int (12 x^{4} - 5 x^{3} - 7) d x

Frequently Asked Questions (FAQ)

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