What is the derivative of f(x)=(4/x)+(1/(5x^3+2x)) ?

The derivative of f(x)=(4/x)+(1/(5x^3+2x)) is (-100x^4-95x^2-18)/(x^2(5x^2+2)^2)

What is the first derivative of f(x)=(4/x)+(1/(5x^3+2x)) ?

The first derivative of f(x)=(4/x)+(1/(5x^3+2x)) is (-100x^4-95x^2-18)/(x^2(5x^2+2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{- 100 x ^{4} - 95 x ^{2} - 18}{x ^{2} ( 5 x ^{2} + 2 ) ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (\frac{1}{5 x ^{3} + 2 x}) = - \frac{15 x ^{2} + 2}{( 5 x ^{3} + 2 x ) ^{2}}

= - \frac{4}{x ^{2}} - \frac{15 x ^{2} + 2}{( 5 x ^{3} + 2 x ) ^{2}}

Simplify

- \frac{4}{x ^{2}} - \frac{15 x ^{2} + 2}{( 5 x ^{3} + 2 x ) ^{2}} : \frac{- 100 x ^{4} - 95 x ^{2} - 18}{x ^{2} ( 5 x ^{2} + 2 ) ^{2}}

= \frac{- 100 x ^{4} - 95 x ^{2} - 18}{x ^{2} ( 5 x ^{2} + 2 ) ^{2}}

\int_{0}^{\frac{π}{2}} sec^{2} (\frac{x}{2}) d x

x y^{^{'}} - 2 y = 0

y^{^{'}} + y = 4 x

\int 2 x + \frac{1}{x ^{2}} + 2 x - 3 d x

\frac{1}{2 x}, 1

What is the derivative of f(x)=(4/x)+(1/(5x^3+2x)) ?
The derivative of f(x)=(4/x)+(1/(5x^3+2x)) is (-100x^4-95x^2-18)/(x^2(5x^2+2)^2)
What is the first derivative of f(x)=(4/x)+(1/(5x^3+2x)) ?
The first derivative of f(x)=(4/x)+(1/(5x^3+2x)) is (-100x^4-95x^2-18)/(x^2(5x^2+2)^2)