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

The derivative of ln(x(x^2+3^3)) is (7x^2+3)/(x(x^2+3))

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

The first derivative of ln(x(x^2+3^3)) is (7x^2+3)/(x(x^2+3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{7 x ^{2} + 3}{x ( x ^{2} + 3 )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{x ( x ^{2} + 3 ) ^{3}} ((x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}) : \frac{7 x ^{2} + 3}{x ( x ^{2} + 3 )}

= \frac{7 x ^{2} + 3}{x ( x ^{2} + 3 )}

What is the derivative of ln(x(x^2+3^3)) ?
The derivative of ln(x(x^2+3^3)) is (7x^2+3)/(x(x^2+3))
What is the first derivative of ln(x(x^2+3^3)) ?
The first derivative of ln(x(x^2+3^3)) is (7x^2+3)/(x(x^2+3))