What is the derivative of ln(x/5) ?

The derivative of ln(x/5) is 1/x

What is the first derivative of ln(x/5) ?

The first derivative of ln(x/5) is 1/x

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\frac{d}{d x} (ln (\frac{x}{5}))

\frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{x}{5}))

Apply the chain rule:

\frac{1}{\frac{x}{5}} \frac{d}{d x} (\frac{x}{5})

= \frac{1}{\frac{x}{5}} \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= \frac{1}{\frac{x}{5}} \cdot \frac{1}{5}

Simplify

\frac{1}{\frac{x}{5}} \cdot \frac{1}{5} : \frac{1}{x}

= \frac{1}{x}

\int 10 x ln (x + 2) d x

\frac{\partial ^{2}}{\partial x \partial y} (x^{5} + x^{2} y + x + 3)

- 7

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 10, y^{^{'}} (0) = b

\int cos (30 x) \cdot cos (4 x) \cdot cos (4 x) d x

What is the derivative of ln(x/5) ?
The derivative of ln(x/5) is 1/x
What is the first derivative of ln(x/5) ?
The first derivative of ln(x/5) is 1/x