What is the derivative of (sqrt(x)/(2e^x)) ?

The derivative of (sqrt(x)/(2e^x)) is (1-2x)/(4e^xsqrt(x))

What is the first derivative of (sqrt(x)/(2e^x)) ?

The first derivative of (sqrt(x)/(2e^x)) is (1-2x)/(4e^xsqrt(x))

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

\frac{1 - 2 x}{4 e ^{x} x}

Solution steps

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

Take the constant out:

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

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

Simplify

\frac{1}{2} \cdot \frac{\frac{1}{2 x} e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}} : \frac{1 - 2 x}{4 e ^{x} x}

= \frac{1 - 2 x}{4 e ^{x} x}

\frac{\partial}{\partial x} (15 x^{2} - 25 x y + 9 y^{2})

x \to 8 lim (5 x + ∣ x - 8 ∣)

\frac{\partial}{\partial x} (2 ln (x) + ln (y))

f (x) = x - 3, (12, 3)

\int_{1}^{4} 1

What is the derivative of (sqrt(x)/(2e^x)) ?
The derivative of (sqrt(x)/(2e^x)) is (1-2x)/(4e^xsqrt(x))
What is the first derivative of (sqrt(x)/(2e^x)) ?
The first derivative of (sqrt(x)/(2e^x)) is (1-2x)/(4e^xsqrt(x))