What is the derivative of ((x+6/(x-6))^5) ?

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

What is the first derivative of ((x+6/(x-6))^5) ?

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

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\frac{d}{d x} ((\frac{x + 6}{x - 6})^{5})

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

Solution steps

\frac{d}{d x} ((\frac{x + 6}{x - 6})^{5})

Apply the chain rule:

5 (\frac{x + 6}{x - 6})^{4} \frac{d}{d x} (\frac{x + 6}{x - 6})

= 5 (\frac{x + 6}{x - 6})^{4} \frac{d}{d x} (\frac{x + 6}{x - 6})

\frac{d}{d x} (\frac{x + 6}{x - 6}) = - \frac{12}{( x - 6 ) ^{2}}

= 5 (\frac{x + 6}{x - 6})^{4} (- \frac{12}{( x - 6 ) ^{2}})

Simplify

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

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

\int x (1 - x^{2})^{5} d x

x = - 5, x = 3, y = 2 x^{2} + 12, y = 0

\int \frac{1}{( x - 2 ) ( x - 5 )} d x

\int 6 x (4 x^{2} - 9)^{2} d x

f (x) = 3 x - 0.6 x ln (x)

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