What is the derivative of (ln(x))/(10x) ?

The derivative of (ln(x))/(10x) is (1-ln(x))/(10x^2)

What is the first derivative of (ln(x))/(10x) ?

The first derivative of (ln(x))/(10x) is (1-ln(x))/(10x^2)

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derivative of

\frac{ln ( x )}{10 x}

\frac{1 - ln ( x )}{10 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{10 x})

Take the constant out:

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

= \frac{1}{10} \frac{d}{d x} (\frac{ln ( x )}{x})

Apply the Quotient Rule:

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

= \frac{1}{10} \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

= \frac{1}{10} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}}

Simplify

\frac{1}{10} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}} : \frac{1 - ln ( x )}{10 x ^{2}}

= \frac{1 - ln ( x )}{10 x ^{2}}

\frac{d}{d x} (\frac{2 x + cos ( 2 x )}{x ^{2} + sin ( 2 x )})

\frac{\partial}{\partial x} ((x^{2} + y^{2}) e^{- x})

x \to 1 lim (\frac{4}{x ^{2} - 1})

\frac{d}{d x} ((3 x + 1)^{4})

\frac{d}{d x} (cos (y) \frac{d y}{d x})

What is the derivative of (ln(x))/(10x) ?
The derivative of (ln(x))/(10x) is (1-ln(x))/(10x^2)
What is the first derivative of (ln(x))/(10x) ?
The first derivative of (ln(x))/(10x) is (1-ln(x))/(10x^2)