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

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

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

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

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derivative of

2 x e^{- 2 x}

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- 2 x}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\int \frac{1}{( x ^{2} - 4 ) ^{\frac{3}{2}}} d x

\int sin (8 x + 2) d x

2 \cdot y^{^{''}} + y^{^{'}} - y = 0

y^{^{''}} + 2 y^{^{'}} = 2 t + 5 - e^{- 2 t}

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

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