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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x^{\frac{1}{3}} y^{\frac{1}{3}})

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2}) - tan (\frac{x}{2}))

\frac{d}{d x} (sec^{4} (2) x^{2})

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

\frac{2 x ^{2} + 8 x + 4}{x}

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