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

The derivative of x/((2x+3)^3) is (3-4x)/((2x+3)^4)

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

The first derivative of x/((2x+3)^3) is (3-4x)/((2x+3)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{3 - 4 x}{( 2 x + 3 ) ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

\frac{1 \cdot ( 2 x + 3 ) ^{3} - 6 ( 2 x + 3 ) ^{2} x}{( ( 2 x + 3 ) ^{3} ) ^{2}} : \frac{3 - 4 x}{( 2 x + 3 ) ^{4}}

= \frac{3 - 4 x}{( 2 x + 3 ) ^{4}}

\frac{\partial}{\partial x} (10 x^{0.5})

\frac{4}{s ^{2}} - \frac{10}{s}

\frac{d}{d x} (\frac{1}{1 + e ^{- x}})

h \to 0 - lim (\frac{2 ^{h} - 1}{h})

x \to 0 lim (- \frac{5}{x})

What is the derivative of x/((2x+3)^3) ?
The derivative of x/((2x+3)^3) is (3-4x)/((2x+3)^4)
What is the first derivative of x/((2x+3)^3) ?
The first derivative of x/((2x+3)^3) is (3-4x)/((2x+3)^4)