What is the derivative of ((x^2+6)/(x^2-6))^4 ?

The derivative of ((x^2+6)/(x^2-6))^4 is -(96x(x^2+6)^3)/((x^2-6)^5)

What is the first derivative of ((x^2+6)/(x^2-6))^4 ?

The first derivative of ((x^2+6)/(x^2-6))^4 is -(96x(x^2+6)^3)/((x^2-6)^5)

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derivative of

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

- \frac{96 x ( x ^{2} + 6 ) ^{3}}{( x ^{2} - 6 ) ^{5}}

Solution steps

\frac{d}{d x} ((\frac{x ^{2} + 6}{x ^{2} - 6})^{4})

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} + 6}{x ^{2} - 6}) = - \frac{24 x}{( x ^{2} - 6 ) ^{2}}

= 4 (\frac{x ^{2} + 6}{x ^{2} - 6})^{3} (- \frac{24 x}{( x ^{2} - 6 ) ^{2}})

Simplify

4 (\frac{x ^{2} + 6}{x ^{2} - 6})^{3} (- \frac{24 x}{( x ^{2} - 6 ) ^{2}}) : - \frac{96 x ( x ^{2} + 6 ) ^{3}}{( x ^{2} - 6 ) ^{5}}

= - \frac{96 x ( x ^{2} + 6 ) ^{3}}{( x ^{2} - 6 ) ^{5}}

(- 2, 5), (3, - 5)

\frac{d}{d x} (7 arctanh (cos (x)))

x \to 2 lim (\frac{x ^{4} - 16}{x ^{3} - 8})

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

\int \frac{5 x ^{2}}{( 121 + x ^{2} ) ^{2}} d x

What is the derivative of ((x^2+6)/(x^2-6))^4 ?
The derivative of ((x^2+6)/(x^2-6))^4 is -(96x(x^2+6)^3)/((x^2-6)^5)
What is the first derivative of ((x^2+6)/(x^2-6))^4 ?
The first derivative of ((x^2+6)/(x^2-6))^4 is -(96x(x^2+6)^3)/((x^2-6)^5)