What is the derivative of f(x)=(8x^2-x+5)/(x+5) ?

The derivative of f(x)=(8x^2-x+5)/(x+5) is (8x^2+80x-10)/((x+5)^2)

What is the first derivative of f(x)=(8x^2-x+5)/(x+5) ?

The first derivative of f(x)=(8x^2-x+5)/(x+5) is (8x^2+80x-10)/((x+5)^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{8 x ^{2} - x + 5}{x + 5}

\frac{8 x ^{2} + 80 x - 10}{( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x ^{2} - x + 5}{x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x ^{2} - x + 5 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( 8 x ^{2} - x + 5 )}{( x + 5 ) ^{2}}

\frac{d}{d x} (8 x^{2} - x + 5) = 16 x - 1

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

= \frac{( 16 x - 1 ) ( x + 5 ) - 1 \cdot ( 8 x ^{2} - x + 5 )}{( x + 5 ) ^{2}}

Simplify

\frac{( 16 x - 1 ) ( x + 5 ) - 1 \cdot ( 8 x ^{2} - x + 5 )}{( x + 5 ) ^{2}} : \frac{8 x ^{2} + 80 x - 10}{( x + 5 ) ^{2}}

= \frac{8 x ^{2} + 80 x - 10}{( x + 5 ) ^{2}}

\frac{d}{d y} (sin (x y^{2}))

\int 6 sin (2 x) + sec^{2} (x) d x

\int e^{13 x} (13) d x

\int 16 cos^{2} (t) d t

x \to 3 lim (\frac{x}{3 - x})

What is the derivative of f(x)=(8x^2-x+5)/(x+5) ?
The derivative of f(x)=(8x^2-x+5)/(x+5) is (8x^2+80x-10)/((x+5)^2)
What is the first derivative of f(x)=(8x^2-x+5)/(x+5) ?
The first derivative of f(x)=(8x^2-x+5)/(x+5) is (8x^2+80x-10)/((x+5)^2)