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

x \to 2 - lim (\frac{m x - 3 m}{x - 3})

\int \frac{4 e ^{x}}{e ^{x} + 3} d x

\frac{d}{d x} (x^{\frac{4}{5}} (x - 4)^{2})

x y + y^{2} - x^{2} \frac{d y}{d x} = 0

\int_{1}^{2} 11 4 x^{2} - 3 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)