What is the derivative of (9ln(x))/x ?

The derivative of (9ln(x))/x is (9(1-ln(x)))/(x^2)

What is the first derivative of (9ln(x))/x ?

The first derivative of (9ln(x))/x is (9(1-ln(x)))/(x^2)

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derivative of

\frac{9 ln ( x )}{x}

\frac{9 ( 1 - ln ( x ) )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 ln ( x )}{x})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{ln ( x )}{x})

Apply the Quotient Rule:

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

= 9 \cdot \frac{\frac{d}{d x} ( ln ( x ) ) x - \frac{d x}{d x} ln ( x )}{x ^{2}}

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

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

= 9 \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}}

Simplify

9 \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}} : \frac{9 ( 1 - ln ( x ) )}{x ^{2}}

= \frac{9 ( 1 - ln ( x ) )}{x ^{2}}

n = 1 \sum \infty ln^{n} (3)

y = 4 - x^{2}, x = - 1, x = 2, y = 0

\frac{d}{d x} (4 - x)

y^{^{'}} = 2 x y^{3}

\frac{d}{d t} (cos (t) + 1)

What is the derivative of (9ln(x))/x ?
The derivative of (9ln(x))/x is (9(1-ln(x)))/(x^2)
What is the first derivative of (9ln(x))/x ?
The first derivative of (9ln(x))/x is (9(1-ln(x)))/(x^2)