What is the derivative of xe^{-(sqrt(3)x/2}) ?

The derivative of xe^{-(sqrt(3)x/2}) is e^{-(sqrt(3)x)/2}-(sqrt(3)e^{-(sqrt(3)x)/2}x)/(2)

What is the first derivative of xe^{-(sqrt(3)x/2}) ?

The first derivative of xe^{-(sqrt(3)x/2}) is e^{-(sqrt(3)x)/2}-(sqrt(3)e^{-(sqrt(3)x)/2}x)/(2)

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Popular >

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

e^{- \frac{3 x}{2}} - \frac{3 e ^{- \frac{3 x}{2}} x}{2}

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{- \frac{3 x}{2}}

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

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

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

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

Simplify

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

= e^{- \frac{3 x}{2}} - \frac{3 e ^{- \frac{3 x}{2}} x}{2}

f (x) = 3 e^{x} + 2 x, at x = 0

\int \frac{2 x}{( 2 - x ) ^{6}} d x

9 π x^{2}

\int \frac{1}{1 + 81 x ^{2}} d x

(2 x sin (y) cos (y)) y^{^{'}} = 4 x^{2} + sin^{2} (y)

What is the derivative of xe^{-(sqrt(3)x/2}) ?
The derivative of xe^{-(sqrt(3)x/2}) is e^{-(sqrt(3)x)/2}-(sqrt(3)e^{-(sqrt(3)x)/2}x)/(2)
What is the first derivative of xe^{-(sqrt(3)x/2}) ?
The first derivative of xe^{-(sqrt(3)x/2}) is e^{-(sqrt(3)x)/2}-(sqrt(3)e^{-(sqrt(3)x)/2}x)/(2)