What is the derivative of ln((7x^2+x/(x^2))) ?

The derivative of ln((7x^2+x/(x^2))) is -1/(x(7x+1))

What is the first derivative of ln((7x^2+x/(x^2))) ?

The first derivative of ln((7x^2+x/(x^2))) is -1/(x(7x+1))

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\frac{d}{d x} (ln (\frac{7 x ^{2} + x}{x ^{2}}))

- \frac{1}{x ( 7 x + 1 )}

Solution steps

\frac{d}{d x} (ln (\frac{7 x ^{2} + x}{x ^{2}}))

Simplify

ln (\frac{7 x ^{2} + x}{x ^{2}}) : ln (\frac{7 x + 1}{x})

= \frac{d}{d x} (ln (\frac{7 x + 1}{x}))

Apply the chain rule:

\frac{1}{\frac{7 x + 1}{x}} \frac{d}{d x} (\frac{7 x + 1}{x})

= \frac{1}{\frac{7 x + 1}{x}} \frac{d}{d x} (\frac{7 x + 1}{x})

\frac{d}{d x} (\frac{7 x + 1}{x}) = - \frac{1}{x ^{2}}

= \frac{1}{\frac{7 x + 1}{x}} (- \frac{1}{x ^{2}})

Simplify

\frac{1}{\frac{7 x + 1}{x}} (- \frac{1}{x ^{2}}) : - \frac{1}{x ( 7 x + 1 )}

= - \frac{1}{x ( 7 x + 1 )}

y = (\frac{x}{5 + x})

\frac{d}{d x} (e^{- 2 x} sin (2 x))

\int_{0}^{1} \frac{1}{x ^{1.5}} d x

y = x + 1

\int 7 x^{2} e^{2 x} d x

What is the derivative of ln((7x^2+x/(x^2))) ?
The derivative of ln((7x^2+x/(x^2))) is -1/(x(7x+1))
What is the first derivative of ln((7x^2+x/(x^2))) ?
The first derivative of ln((7x^2+x/(x^2))) is -1/(x(7x+1))