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

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

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

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

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derivative of

1 + x e^{- 2 x}

\frac{- 2 e ^{- 2 x} x + e ^{- 2 x}}{2 1 + e ^{- 2 x} x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

7 (x - 5)^{\frac{2}{3}}

\int_{\frac{1}{2}}^{7} 6 x ln (2 x) d x

\int_{- \infty}^{- 1} e^{- 2 t} d t

\frac{d}{d y} (ln (x + y))

f (x) = 2^{40}

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