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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{- t ^{2} + 2 t + 3} d t

a re a 4 x^{2} + y = 4, x^{8} - y = 1

\int_{1}^{5} (x - 1)^{2} d x

\int \frac{12}{x ^{2}} d x

\frac{d}{d x} (x - \frac{1}{3} x)

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