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

The derivative of ((x+5)/(x-5))^5 is -(50(x+5)^4)/((x-5)^6)

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

The first derivative of ((x+5)/(x-5))^5 is -(50(x+5)^4)/((x-5)^6)

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derivative of

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

- \frac{50 ( x + 5 ) ^{4}}{( x - 5 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

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

= 5 (\frac{x + 5}{x - 5})^{4} (- \frac{10}{( x - 5 ) ^{2}})

Simplify

5 (\frac{x + 5}{x - 5})^{4} (- \frac{10}{( x - 5 ) ^{2}}) : - \frac{50 ( x + 5 ) ^{4}}{( x - 5 ) ^{6}}

= - \frac{50 ( x + 5 ) ^{4}}{( x - 5 ) ^{6}}

x \to 0 + lim (\frac{1}{x ^{2} - x})

\int x^{3} 7 - x^{2} d x

\frac{d}{d x} (5 + sin (x))

\int \frac{ln ( x )}{x ^{4}} d x

\frac{\partial}{\partial x} (\frac{x ^{2} - y ^{2}}{1 + x ^{2}})

What is the derivative of ((x+5)/(x-5))^5 ?
The derivative of ((x+5)/(x-5))^5 is -(50(x+5)^4)/((x-5)^6)
What is the first derivative of ((x+5)/(x-5))^5 ?
The first derivative of ((x+5)/(x-5))^5 is -(50(x+5)^4)/((x-5)^6)