What is the derivative of f(x)=(ln(x))/(13+x) ?

The derivative of f(x)=(ln(x))/(13+x) is (13+x-xln(x))/(x(13+x)^2)

What is the first derivative of f(x)=(ln(x))/(13+x) ?

The first derivative of f(x)=(ln(x))/(13+x) is (13+x-xln(x))/(x(13+x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{ln ( x )}{13 + x}

\frac{13 + x - x ln ( x )}{x ( 13 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{13 + x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( x ) ) ( 13 + x ) - \frac{d}{d x} ( 13 + x ) ln ( x )}{( 13 + x ) ^{2}}

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

\frac{d}{d x} (13 + x) = 1

= \frac{\frac{1}{x} ( 13 + x ) - 1 \cdot ln ( x )}{( 13 + x ) ^{2}}

Simplify

\frac{\frac{1}{x} ( 13 + x ) - 1 \cdot ln ( x )}{( 13 + x ) ^{2}} : \frac{13 + x - x ln ( x )}{x ( 13 + x ) ^{2}}

= \frac{13 + x - x ln ( x )}{x ( 13 + x ) ^{2}}

\int_{1}^{12} 2 x d x

\int \frac{9 e ^{2 t}}{1 + e ^{4 t}} d t

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

\int co tan (x) d x

x \to \frac{π}{3} lim (x cos (x))

What is the derivative of f(x)=(ln(x))/(13+x) ?
The derivative of f(x)=(ln(x))/(13+x) is (13+x-xln(x))/(x(13+x)^2)
What is the first derivative of f(x)=(ln(x))/(13+x) ?
The first derivative of f(x)=(ln(x))/(13+x) is (13+x-xln(x))/(x(13+x)^2)