What is the derivative of (log_{e}(x)/(x^2)) ?

The derivative of (log_{e}(x)/(x^2)) is (1-2ln(x))/(x^3)

What is the first derivative of (log_{e}(x)/(x^2)) ?

The first derivative of (log_{e}(x)/(x^2)) is (1-2ln(x))/(x^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} (\frac{lo g _{e} ( x )}{x ^{2}})

\frac{1 - 2 ln ( x )}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{lo g _{e} ( x )}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( lo g _{e} ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) lo g _{e} ( x )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (lo g_{e} (x)) = \frac{1}{x}

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

= \frac{\frac{1}{x} x ^{2} - 2 x lo g _{e} ( x )}{( x ^{2} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{2} - 2 x lo g _{e} ( x )}{( x ^{2} ) ^{2}} : \frac{1 - 2 ln ( x )}{x ^{3}}

= \frac{1 - 2 ln ( x )}{x ^{3}}

y^{^{''}} - 2 y^{^{'}} - 3 y = 0

f (t) = t

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

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

\int \frac{1}{2 + 5 x ^{6}} (30 x^{5}) d x

What is the derivative of (log_{e}(x)/(x^2)) ?
The derivative of (log_{e}(x)/(x^2)) is (1-2ln(x))/(x^3)
What is the first derivative of (log_{e}(x)/(x^2)) ?
The first derivative of (log_{e}(x)/(x^2)) is (1-2ln(x))/(x^3)