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}}

\frac{d}{d x} ((ln (9))^{x})

\int (ln (y)) d y

\int \frac{( 5 x + 7 )}{( x ^{2} + 4 x + 4 )} d x

(x + 3)

\int \frac{1}{sin ( \frac{x}{a} )} 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)