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

The derivative of ((ln(x)^2)/(e^x)) is (ln(x)(2-xln(x)))/(e^xx)

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

The first derivative of ((ln(x)^2)/(e^x)) is (ln(x)(2-xln(x)))/(e^xx)

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

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

Solution steps

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

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

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

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

Simplify

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

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

f (x) = 8 sin (2 x)

\int \frac{1}{b - a} d x

\int 1 + 3 x d x

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

\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 500 x)

What is the derivative of ((ln(x)^2)/(e^x)) ?
The derivative of ((ln(x)^2)/(e^x)) is (ln(x)(2-xln(x)))/(e^xx)
What is the first derivative of ((ln(x)^2)/(e^x)) ?
The first derivative of ((ln(x)^2)/(e^x)) is (ln(x)(2-xln(x)))/(e^xx)