What is the derivative of ((x+7/(x-7))^5) ?

The derivative of ((x+7/(x-7))^5) is -(70(x+7)^4)/((x-7)^6)

What is the first derivative of ((x+7/(x-7))^5) ?

The first derivative of ((x+7/(x-7))^5) is -(70(x+7)^4)/((x-7)^6)

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\frac{d}{d x} ((\frac{x + 7}{x - 7})^{5})

- \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{x + 7}{x - 7})^{5})

Apply the chain rule:

5 (\frac{x + 7}{x - 7})^{4} \frac{d}{d x} (\frac{x + 7}{x - 7})

= 5 (\frac{x + 7}{x - 7})^{4} \frac{d}{d x} (\frac{x + 7}{x - 7})

\frac{d}{d x} (\frac{x + 7}{x - 7}) = - \frac{14}{( x - 7 ) ^{2}}

= 5 (\frac{x + 7}{x - 7})^{4} (- \frac{14}{( x - 7 ) ^{2}})

Simplify

5 (\frac{x + 7}{x - 7})^{4} (- \frac{14}{( x - 7 ) ^{2}}) : - \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

= - \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

d er i v a t i v e (x + 3)

x \to 0 + lim (\frac{- 1}{14 x})

\int (sec (\frac{x}{24}))^{2} tan (\frac{x}{24}) d x

h \to 0 lim (\frac{sinh ( x )}{h})

\int 2 cos (ln (x)) d x

What is the derivative of ((x+7/(x-7))^5) ?
The derivative of ((x+7/(x-7))^5) is -(70(x+7)^4)/((x-7)^6)
What is the first derivative of ((x+7/(x-7))^5) ?
The first derivative of ((x+7/(x-7))^5) is -(70(x+7)^4)/((x-7)^6)