What is the derivative of (20x/(x^2-5)) ?

The derivative of (20x/(x^2-5)) is (20(-x^2-5))/((x^2-5)^2)

What is the first derivative of (20x/(x^2-5)) ?

The first derivative of (20x/(x^2-5)) is (20(-x^2-5))/((x^2-5)^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{20 x}{x ^{2} - 5})

\frac{20 ( - x ^{2} - 5 )}{( x ^{2} - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{20 x}{x ^{2} - 5})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 20 \frac{d}{d x} (\frac{x}{x ^{2} - 5})

Apply the Quotient Rule:

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

= 20 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 5 ) - \frac{d}{d x} ( x ^{2} - 5 ) x}{( x ^{2} - 5 ) ^{2}}

\frac{d x}{d x} = 1

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

= 20 \cdot \frac{1 \cdot ( x ^{2} - 5 ) - 2 xx}{( x ^{2} - 5 ) ^{2}}

Simplify

20 \cdot \frac{1 \cdot ( x ^{2} - 5 ) - 2 xx}{( x ^{2} - 5 ) ^{2}} : \frac{20 ( - x ^{2} - 5 )}{( x ^{2} - 5 ) ^{2}}

= \frac{20 ( - x ^{2} - 5 )}{( x ^{2} - 5 ) ^{2}}

(x^{\frac{3}{2}})^{^{'}}

\frac{d}{d x} (\frac{3 x ^{2} - 3}{2 x})

\int 2 x^{2} e^{x} d x

y^{^{'}} = 1 + 9 x - 5 y, y (1) = 2

\frac{\partial}{\partial y} (ln (x^{2} + y^{2}))

What is the derivative of (20x/(x^2-5)) ?
The derivative of (20x/(x^2-5)) is (20(-x^2-5))/((x^2-5)^2)
What is the first derivative of (20x/(x^2-5)) ?
The first derivative of (20x/(x^2-5)) is (20(-x^2-5))/((x^2-5)^2)