What is the derivative of ln(1+3/x+5/(x^2)) ?

The derivative of ln(1+3/x+5/(x^2)) is (-3x-10)/(x(x^2+3x+5))

What is the first derivative of ln(1+3/x+5/(x^2)) ?

The first derivative of ln(1+3/x+5/(x^2)) is (-3x-10)/(x(x^2+3x+5))

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derivative of

ln (1 + \frac{3}{x} + \frac{5}{x ^{2}})

\frac{- 3 x - 10}{x ( x ^{2} + 3 x + 5 )}

Solution steps

\frac{d}{d x} (ln (1 + \frac{3}{x} + \frac{5}{x ^{2}}))

Apply the chain rule:

\frac{1}{1 + \frac{3}{x} + \frac{5}{x ^{2}}} \frac{d}{d x} (1 + \frac{3}{x} + \frac{5}{x ^{2}})

= \frac{1}{1 + \frac{3}{x} + \frac{5}{x ^{2}}} \frac{d}{d x} (1 + \frac{3}{x} + \frac{5}{x ^{2}})

\frac{d}{d x} (1 + \frac{3}{x} + \frac{5}{x ^{2}}) = - \frac{3}{x ^{2}} - \frac{10}{x ^{3}}

= \frac{1}{1 + \frac{3}{x} + \frac{5}{x ^{2}}} (- \frac{3}{x ^{2}} - \frac{10}{x ^{3}})

Simplify

\frac{1}{1 + \frac{3}{x} + \frac{5}{x ^{2}}} (- \frac{3}{x ^{2}} - \frac{10}{x ^{3}}) : \frac{- 3 x - 10}{x ( x ^{2} + 3 x + 5 )}

= \frac{- 3 x - 10}{x ( x ^{2} + 3 x + 5 )}

\int (x^{4} + 3)^{\frac{3}{2}} x^{3} d x

\frac{\partial}{\partial b} (m x^{b})

\int 8 y d y

\int 4 sin (4 x) sin (3 x) cos (2 x) d x

\frac{\partial}{\partial x} (e^{- 3 y} cos (3 x))

What is the derivative of ln(1+3/x+5/(x^2)) ?
The derivative of ln(1+3/x+5/(x^2)) is (-3x-10)/(x(x^2+3x+5))
What is the first derivative of ln(1+3/x+5/(x^2)) ?
The first derivative of ln(1+3/x+5/(x^2)) is (-3x-10)/(x(x^2+3x+5))