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

The derivative of (3x^2/(ln(x))) is (3(2xln(x)-x))/(ln^2(x))

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

The first derivative of (3x^2/(ln(x))) is (3(2xln(x)-x))/(ln^2(x))

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{3 x ^{2}}{ln ( x )})

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = (x + y)^{2} - 1, y (3) = 4

\int_{0}^{1} 2 (1 + x)^{8} d x

\frac{( x + 2 )}{( x - 2 )}

x \to 3 lim (\frac{2 ^{x} - 8}{3 - x})

y = 4 x, y = 4, y = \frac{4}{9} x^{2} 4

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