What is the derivative of sqrt(e^{2x)+4e^{-4x}+1} ?

The derivative of sqrt(e^{2x)+4e^{-4x}+1} is (e^{-4x}(e^{6x}-8))/(sqrt(e^{2x)+4e^{-4x)+1}}

What is the first derivative of sqrt(e^{2x)+4e^{-4x}+1} ?

The first derivative of sqrt(e^{2x)+4e^{-4x}+1} is (e^{-4x}(e^{6x}-8))/(sqrt(e^{2x)+4e^{-4x)+1}}

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\frac{d}{d x} (e^{2 x} + 4 e^{- 4 x} + 1)

\frac{e ^{- 4 x} ( e ^{6 x} - 8 )}{e ^{2 x} + 4 e ^{- 4 x} + 1}

Solution steps

\frac{d}{d x} (e^{2 x} + 4 e^{- 4 x} + 1)

Apply the chain rule:

\frac{1}{2 e ^{2 x} + 4 e ^{- 4 x} + 1} \frac{d}{d x} (e^{2 x} + 4 e^{- 4 x} + 1)

= \frac{1}{2 e ^{2 x} + 4 e ^{- 4 x} + 1} \frac{d}{d x} (e^{2 x} + 4 e^{- 4 x} + 1)

\frac{d}{d x} (e^{2 x} + 4 e^{- 4 x} + 1) = - 16 e^{- 4 x} + 2 e^{2 x}

= \frac{1}{2 e ^{2 x} + 4 e ^{- 4 x} + 1} (- 16 e^{- 4 x} + 2 e^{2 x})

Simplify

\frac{1}{2 e ^{2 x} + 4 e ^{- 4 x} + 1} (- 16 e^{- 4 x} + 2 e^{2 x}) : \frac{e ^{- 4 x} ( e ^{6 x} - 8 )}{e ^{2 x} + 4 e ^{- 4 x} + 1}

= \frac{e ^{- 4 x} ( e ^{6 x} - 8 )}{e ^{2 x} + 4 e ^{- 4 x} + 1}

\int_{1}^{2} \frac{13}{x ^{3} + 4 x} d x

f (x) = x x, (16, 64)

\frac{d}{d x} (e^{x} cos (3 x) - 3 e^{x} sin (3 x))

\int_{0}^{5} π (x^{2}) d x

\int \frac{1}{4 x ^{2} + 10 x + 5} d x

What is the derivative of sqrt(e^{2x)+4e^{-4x}+1} ?
The derivative of sqrt(e^{2x)+4e^{-4x}+1} is (e^{-4x}(e^{6x}-8))/(sqrt(e^{2x)+4e^{-4x)+1}}
What is the first derivative of sqrt(e^{2x)+4e^{-4x}+1} ?
The first derivative of sqrt(e^{2x)+4e^{-4x}+1} is (e^{-4x}(e^{6x}-8))/(sqrt(e^{2x)+4e^{-4x)+1}}