What is the derivative of y=((x^2+6)/(x^2-6))^3 ?

The derivative of y=((x^2+6)/(x^2-6))^3 is -(72x(x^2+6)^2)/((x^2-6)^4)

What is the first derivative of y=((x^2+6)/(x^2-6))^3 ?

The first derivative of y=((x^2+6)/(x^2-6))^3 is -(72x(x^2+6)^2)/((x^2-6)^4)

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derivative of

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

- \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

Simplify

3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} (- \frac{24 x}{( x ^{2} - 6 ) ^{2}}) : - \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

= - \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

\frac{d}{d x} (arcsin (3 x) + arccos (3 x))

\frac{\partial}{\partial x} (sin (θ))

\frac{d}{d x} (arccot (\frac{x}{8}))

x \to 0 lim ((1 + x)^{\frac{3}{x}})

y^{^{''}} - \frac{5}{t} y^{^{'}} + \frac{18}{t ^{2}} y = 0

What is the derivative of y=((x^2+6)/(x^2-6))^3 ?
The derivative of y=((x^2+6)/(x^2-6))^3 is -(72x(x^2+6)^2)/((x^2-6)^4)
What is the first derivative of y=((x^2+6)/(x^2-6))^3 ?
The first derivative of y=((x^2+6)/(x^2-6))^3 is -(72x(x^2+6)^2)/((x^2-6)^4)