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

The derivative of ln(((x+2)/(x^2))) is (-x-4)/(x(x+2))

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

The first derivative of ln(((x+2)/(x^2))) is (-x-4)/(x(x+2))

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

\frac{- x - 4}{x ( x + 2 )}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{\frac{x + 2}{x ^{2}}} \cdot \frac{- x - 4}{x ^{3}}

Simplify

\frac{1}{\frac{x + 2}{x ^{2}}} \cdot \frac{- x - 4}{x ^{3}} : \frac{- x - 4}{x ( x + 2 )}

= \frac{- x - 4}{x ( x + 2 )}

y^{^{'}} - y = 9 t e^{2 t}

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

f (x) = x e^{x^{2}}

\frac{5 x ^{2} tan ( x )}{sec ( x )}

\int \frac{x ^{2}}{x - 9} d x

What is the derivative of ln(((x+2)/(x^2))) ?
The derivative of ln(((x+2)/(x^2))) is (-x-4)/(x(x+2))
What is the first derivative of ln(((x+2)/(x^2))) ?
The first derivative of ln(((x+2)/(x^2))) is (-x-4)/(x(x+2))