What is the derivative of sqrt((5x+1/(2x^2+1))) ?

The derivative of sqrt((5x+1/(2x^2+1))) is (-10x^2-4x+5)/(2sqrt(5x+1)(2x^2+1)^{3/2)}

What is the first derivative of sqrt((5x+1/(2x^2+1))) ?

The first derivative of sqrt((5x+1/(2x^2+1))) is (-10x^2-4x+5)/(2sqrt(5x+1)(2x^2+1)^{3/2)}

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{5 x + 1}{2 x ^{2} + 1})

\frac{- 10 x ^{2} - 4 x + 5}{2 5 x + 1 ( 2 x ^{2} + 1 ) ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{5 x + 1}{2 x ^{2} + 1}) = \frac{- 10 x ^{2} - 4 x + 5}{( 2 x ^{2} + 1 ) ^{2}}

= \frac{1}{2 \frac{5 x + 1}{2 x ^{2} + 1}} \cdot \frac{- 10 x ^{2} - 4 x + 5}{( 2 x ^{2} + 1 ) ^{2}}

Simplify

\frac{1}{2 \frac{5 x + 1}{2 x ^{2} + 1}} \cdot \frac{- 10 x ^{2} - 4 x + 5}{( 2 x ^{2} + 1 ) ^{2}} : \frac{- 10 x ^{2} - 4 x + 5}{2 5 x + 1 ( 2 x ^{2} + 1 ) ^{\frac{3}{2}}}

= \frac{- 10 x ^{2} - 4 x + 5}{2 5 x + 1 ( 2 x ^{2} + 1 ) ^{\frac{3}{2}}}

x \to \infty lim (\frac{3 x ^{2} + 2 x - 8}{4 x ^{4} - 5 x + 4})

x \to 0 lim (\frac{1}{x + 1})

\int (\frac{1}{3}) x^{3} - 5 x d x

\frac{d}{d x} (9 e^{3 x} x + 6 e^{3 x})

\int (6 x^{2} - 4 x + 5) d x

What is the derivative of sqrt((5x+1/(2x^2+1))) ?
The derivative of sqrt((5x+1/(2x^2+1))) is (-10x^2-4x+5)/(2sqrt(5x+1)(2x^2+1)^{3/2)}
What is the first derivative of sqrt((5x+1/(2x^2+1))) ?
The first derivative of sqrt((5x+1/(2x^2+1))) is (-10x^2-4x+5)/(2sqrt(5x+1)(2x^2+1)^{3/2)}