What is the derivative of (x^2+sqrt(x)/(2x+5)) ?

The derivative of (x^2+sqrt(x)/(2x+5)) is (4x^2sqrt(x)+20xsqrt(x)-2x+5)/(2sqrt(x)(2x+5)^2)

What is the first derivative of (x^2+sqrt(x)/(2x+5)) ?

The first derivative of (x^2+sqrt(x)/(2x+5)) is (4x^2sqrt(x)+20xsqrt(x)-2x+5)/(2sqrt(x)(2x+5)^2)

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{x ^{2} + x}{2 x + 5})

\frac{4 x ^{2} x + 20 x x - 2 x + 5}{2 x ( 2 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + x}{2 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + x ) ( 2 x + 5 ) - \frac{d}{d x} ( 2 x + 5 ) ( x ^{2} + x )}{( 2 x + 5 ) ^{2}}

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

\frac{d}{d x} (2 x + 5) = 2

= \frac{( 2 x + \frac{1}{2 x} ) ( 2 x + 5 ) - 2 ( x ^{2} + x )}{( 2 x + 5 ) ^{2}}

Simplify

\frac{( 2 x + \frac{1}{2 x} ) ( 2 x + 5 ) - 2 ( x ^{2} + x )}{( 2 x + 5 ) ^{2}} : \frac{4 x ^{2} x + 20 x x - 2 x + 5}{2 x ( 2 x + 5 ) ^{2}}

= \frac{4 x ^{2} x + 20 x x - 2 x + 5}{2 x ( 2 x + 5 ) ^{2}}

x \to - \infty lim (\frac{x}{- x})

12 x^{\frac{1}{2}}

x \to a lim (2 x - 1)

- \frac{40 ( 9 + 5 x ^{2} )}{( 9 - 5 x ^{2} ) ^{2}}

\int_{1}^{4} 2 x 5 + x^{2} d x

What is the derivative of (x^2+sqrt(x)/(2x+5)) ?
The derivative of (x^2+sqrt(x)/(2x+5)) is (4x^2sqrt(x)+20xsqrt(x)-2x+5)/(2sqrt(x)(2x+5)^2)
What is the first derivative of (x^2+sqrt(x)/(2x+5)) ?
The first derivative of (x^2+sqrt(x)/(2x+5)) is (4x^2sqrt(x)+20xsqrt(x)-2x+5)/(2sqrt(x)(2x+5)^2)