What is the derivative of (sqrt(x))/(e^x) ?

The derivative of (sqrt(x))/(e^x) is (1-2x)/(2e^xsqrt(x))

What is the first derivative of (sqrt(x))/(e^x) ?

The first derivative of (sqrt(x))/(e^x) is (1-2x)/(2e^xsqrt(x))

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derivative of

\frac{x}{e ^{x}}

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

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

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

\int \frac{( x ^{3} + 6 x ^{2} + 2 x + 3 )}{x ^{2} + 6 x + 1} d x

5 x y^{^{'}} + y = 30 x

\frac{d}{d x} (arcsin (7 x))

\int x^{9} \cdot ln (x) d x

e^{2 l n (x)}

What is the derivative of (sqrt(x))/(e^x) ?
The derivative of (sqrt(x))/(e^x) is (1-2x)/(2e^xsqrt(x))
What is the first derivative of (sqrt(x))/(e^x) ?
The first derivative of (sqrt(x))/(e^x) is (1-2x)/(2e^xsqrt(x))