What is the (x/(sqrt(x^5+1)))^' ?

The (x/(sqrt(x^5+1)))^' is (-3x^5+2)/(2(x^5+1)sqrt(x^5+1))

What is the first (x/(sqrt(x^5+1)))^' ?

The first (x/(sqrt(x^5+1)))^' is (-3x^5+2)/(2(x^5+1)sqrt(x^5+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\frac{x}{x ^{5} + 1})^{^{'}}

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

Solution steps

(\frac{x}{x ^{5} + 1})^{'}

Apply the Quotient Rule:

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

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

x^{'} = 1

(x^{5} + 1)^{'} = \frac{5 x ^{4}}{2 x ^{5} + 1}

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

Simplify

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

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

f (v) = (v^{- 3} + 3 v^{- 2})^{3}

f^{^{'}} (x) = 7 x^{4}

x \to - 3 lim (x^{2} + 7 x - 6)

x \to 9 + lim (\frac{6}{x - 9})

f (x) = x 5 - x

What is the (x/(sqrt(x^5+1)))^' ?
The (x/(sqrt(x^5+1)))^' is (-3x^5+2)/(2(x^5+1)sqrt(x^5+1))
What is the first (x/(sqrt(x^5+1)))^' ?
The first (x/(sqrt(x^5+1)))^' is (-3x^5+2)/(2(x^5+1)sqrt(x^5+1))