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

The derivative of f(x)=((x+3)/(x-3))^5 is -(30(x+3)^4)/((x-3)^6)

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

The first derivative of f(x)=((x+3)/(x-3))^5 is -(30(x+3)^4)/((x-3)^6)

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derivative of

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

- \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

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

= 5 (\frac{x + 3}{x - 3})^{4} (- \frac{6}{( x - 3 ) ^{2}})

Simplify

5 (\frac{x + 3}{x - 3})^{4} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

= - \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

\int (x + \frac{1}{x ^{3}}) d x

n = 1 \sum \infty \frac{1}{2} (0.3)^{n}

f (x) = \frac{3}{x}, at x = - 5

\frac{( s ^{2} )}{s ^{2} + 1}

\int \frac{1 - x ^{2}}{1 - 2 x} d x

What is the derivative of f(x)=((x+3)/(x-3))^5 ?
The derivative of f(x)=((x+3)/(x-3))^5 is -(30(x+3)^4)/((x-3)^6)
What is the first derivative of f(x)=((x+3)/(x-3))^5 ?
The first derivative of f(x)=((x+3)/(x-3))^5 is -(30(x+3)^4)/((x-3)^6)