What is the derivative of f(x)=((6ln(x)))/x ?

The derivative of f(x)=((6ln(x)))/x is (6(1-ln(x)))/(x^2)

What is the first derivative of f(x)=((6ln(x)))/x ?

The first derivative of f(x)=((6ln(x)))/x is (6(1-ln(x)))/(x^2)

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derivative of

f (x) = \frac{( 6 ln ( x ) )}{x}

\frac{6 ( 1 - ln ( x ) )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 ln ( x )}{x})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{ln ( x )}{x})

Apply the Quotient Rule:

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

= 6 \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

= 6 \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}}

Simplify

6 \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}} : \frac{6 ( 1 - ln ( x ) )}{x ^{2}}

= \frac{6 ( 1 - ln ( x ) )}{x ^{2}}

\int e^{(- x)} d x

\frac{d}{d x} (\frac{1}{2} x^{3})

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

77 p + 20 - 360, at 75

\frac{d}{d x} (arctan (3 x + 2))

What is the derivative of f(x)=((6ln(x)))/x ?
The derivative of f(x)=((6ln(x)))/x is (6(1-ln(x)))/(x^2)
What is the first derivative of f(x)=((6ln(x)))/x ?
The first derivative of f(x)=((6ln(x)))/x is (6(1-ln(x)))/(x^2)