What is the derivative of ((x^2+3)/(x^2-3))^5 ?

The derivative of ((x^2+3)/(x^2-3))^5 is -(60x(x^2+3)^4)/((x^2-3)^6)

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

The first derivative of ((x^2+3)/(x^2-3))^5 is -(60x(x^2+3)^4)/((x^2-3)^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

- \frac{60 x ( x ^{2} + 3 ) ^{4}}{( x ^{2} - 3 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3}) = - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

= 5 (\frac{x ^{2} + 3}{x ^{2} - 3})^{4} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

Simplify

5 (\frac{x ^{2} + 3}{x ^{2} - 3})^{4} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{60 x ( x ^{2} + 3 ) ^{4}}{( x ^{2} - 3 ) ^{6}}

= - \frac{60 x ( x ^{2} + 3 ) ^{4}}{( x ^{2} - 3 ) ^{6}}

\frac{d}{d x} (\frac{x ^{4}}{2 - x ^{3}})

\int \frac{π}{12} sin (\frac{π x}{6}) d x

\frac{d}{d x} (csc (x) (x + cot (x)))

2 sin (x^{2})

What is the derivative of ((x^2+3)/(x^2-3))^5 ?
The derivative of ((x^2+3)/(x^2-3))^5 is -(60x(x^2+3)^4)/((x^2-3)^6)
What is the first derivative of ((x^2+3)/(x^2-3))^5 ?
The first derivative of ((x^2+3)/(x^2-3))^5 is -(60x(x^2+3)^4)/((x^2-3)^6)