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}

\int x e^{- x (y + 1)} d x

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

\frac{d y}{d x} + y cos (x) = 2 cos (x), y (0) = 4

d er i v a t i v e sec (θ)

\int 4 x ln (2 x) 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)