What is the derivative of ln(1+3/x) ?

The derivative of ln(1+3/x) is -3/(x(x+3))

What is the first derivative of ln(1+3/x) ?

The first derivative of ln(1+3/x) is -3/(x(x+3))

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\frac{d}{d x} (ln (1 + \frac{3}{x}))

- \frac{3}{x ( x + 3 )}

Solution steps

\frac{d}{d x} (ln (1 + \frac{3}{x}))

Apply the chain rule:

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

= \frac{1}{1 + \frac{3}{x}} \frac{d}{d x} (1 + \frac{3}{x})

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

= \frac{1}{1 + \frac{3}{x}} (- \frac{3}{x ^{2}})

Simplify

\frac{1}{1 + \frac{3}{x}} (- \frac{3}{x ^{2}}) : - \frac{3}{x ( x + 3 )}

= - \frac{3}{x ( x + 3 )}

(x^{2} + 1) y^{^{'}} = - 4 x (y - 1), y (0) = 8

\int 4 e^{5} d x

x \to 0 lim (\frac{e ^{\frac{1}{x}}}{x})

t^{2} y^{^{'}} - t = 1 + y + t y

\int \frac{x + 5}{x ^{2} + 4 x + 8} d x

What is the derivative of ln(1+3/x) ?
The derivative of ln(1+3/x) is -3/(x(x+3))
What is the first derivative of ln(1+3/x) ?
The first derivative of ln(1+3/x) is -3/(x(x+3))