What is the derivative of (2(1-ln(x)))/(x^2) ?

The derivative of (2(1-ln(x)))/(x^2) is -(2(-2ln(x)+3))/(x^3)

What is the first derivative of (2(1-ln(x)))/(x^2) ?

The first derivative of (2(1-ln(x)))/(x^2) is -(2(-2ln(x)+3))/(x^3)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

2 \cdot \frac{( - \frac{1}{x} ) x ^{2} - 2 x ( 1 - ln ( x ) )}{( x ^{2} ) ^{2}} : - \frac{2 ( - 2 ln ( x ) + 3 )}{x ^{3}}

= - \frac{2 ( - 2 ln ( x ) + 3 )}{x ^{3}}

x \to - 2 lim (3 x^{2} + 5 x - 1)

\int \frac{t}{( t ^{2} + 1 ) ^{\frac{5}{2}}} d t

\int \frac{1}{16 x ^{2} + 7} d x

\frac{13}{x}

\frac{d}{d t} (e^{7 t s i n (2 t)})

What is the derivative of (2(1-ln(x)))/(x^2) ?
The derivative of (2(1-ln(x)))/(x^2) is -(2(-2ln(x)+3))/(x^3)
What is the first derivative of (2(1-ln(x)))/(x^2) ?
The first derivative of (2(1-ln(x)))/(x^2) is -(2(-2ln(x)+3))/(x^3)