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

The derivative of (ln(x))/(e^x) is (1-xln(x))/(e^xx)

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

The first derivative of (ln(x))/(e^x) is (1-xln(x))/(e^xx)

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derivative of

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

\frac{1 - x ln ( x )}{e ^{x} x}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{5}{x} - \frac{5}{∣ x ∣})

f (x) = x, g (x) = x, [0, 2]

\int_{2}^{25} sin (2 x) d x

\frac{\partial}{\partial x} (d x)

\int (6 x + 8) d x

What is the derivative of (ln(x))/(e^x) ?
The derivative of (ln(x))/(e^x) is (1-xln(x))/(e^xx)
What is the first derivative of (ln(x))/(e^x) ?
The first derivative of (ln(x))/(e^x) is (1-xln(x))/(e^xx)