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

The derivative of ln((5x^2+3/(x^2))) is -6/(x(5x^2+3))

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

The first derivative of ln((5x^2+3/(x^2))) is -6/(x(5x^2+3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

- \frac{6}{x ( 5 x ^{2} + 3 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{5 x ^{2} + 3}{x ^{2}}) = - \frac{6}{x ^{3}}

= \frac{1}{\frac{5 x ^{2} + 3}{x ^{2}}} (- \frac{6}{x ^{3}})

Simplify

\frac{1}{\frac{5 x ^{2} + 3}{x ^{2}}} (- \frac{6}{x ^{3}}) : - \frac{6}{x ( 5 x ^{2} + 3 )}

= - \frac{6}{x ( 5 x ^{2} + 3 )}

3 x y^{^{'}} + 7 y = 0, y (1) = 8

\int 2 (2 x + 1) 6 d x

y^{^{''}} + 8 y^{^{'}} - 9 y = 0

(z^{2} + e^{z}) z

\frac{d y}{d x} = - 2 y + x, y (0) = 0

What is the derivative of ln((5x^2+3/(x^2))) ?
The derivative of ln((5x^2+3/(x^2))) is -6/(x(5x^2+3))
What is the first derivative of ln((5x^2+3/(x^2))) ?
The first derivative of ln((5x^2+3/(x^2))) is -6/(x(5x^2+3))