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

The derivative of f(x)=(x^3+5)/(x^2+1) is (x^4+3x^2-10x)/((x^2+1)^2)

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

\frac{d}{d x} (arccos (2 x^{2}))

\int 2 + t^{2} d t

\int \frac{8}{x ^{2} x ^{2} + 25} d x

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

\int (1 - x^{2}) d x

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