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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\frac{d}{d x} ((\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}}

\int sin (3 x) tan (3 x) d x

n = 2 \sum \infty n e^{- 2 n}

f (x) = sin (2 x^{2})

\int_{0}^{2} 2 π x (1 + \frac{x ^{2}}{2}) d x

x \to 1 lim (x^{2} + 8 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)