What is the derivative of (7+2ln(x)/x) ?

The derivative of (7+2ln(x)/x) is (-2ln(x)-5)/(x^2)

What is the first derivative of (7+2ln(x)/x) ?

The first derivative of (7+2ln(x)/x) is (-2ln(x)-5)/(x^2)

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\frac{d}{d x} (\frac{7 + 2 ln ( x )}{x})

\frac{- 2 ln ( x ) - 5}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 + 2 ln ( x )}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 + 2 ln ( x ) ) x - \frac{d x}{d x} ( 7 + 2 ln ( x ) )}{x ^{2}}

\frac{d}{d x} (7 + 2 ln (x)) = \frac{2}{x}

\frac{d x}{d x} = 1

= \frac{\frac{2}{x} x - 1 \cdot ( 7 + 2 ln ( x ) )}{x ^{2}}

Simplify

\frac{\frac{2}{x} x - 1 \cdot ( 7 + 2 ln ( x ) )}{x ^{2}} : \frac{- 2 ln ( x ) - 5}{x ^{2}}

= \frac{- 2 ln ( x ) - 5}{x ^{2}}

\int (csc (x) cot (x)) d x

d er i v a t i v e y = e^{x}

x \to \infty lim (6 \cdot x)

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

\frac{d}{d j} (3 i - 4 j)

What is the derivative of (7+2ln(x)/x) ?
The derivative of (7+2ln(x)/x) is (-2ln(x)-5)/(x^2)
What is the first derivative of (7+2ln(x)/x) ?
The first derivative of (7+2ln(x)/x) is (-2ln(x)-5)/(x^2)