What is the derivative of y=((x^2+3)/(x^2-3))^7 ?

The derivative of y=((x^2+3)/(x^2-3))^7 is -(84x(x^2+3)^6)/((x^2-3)^8)

What is the first derivative of y=((x^2+3)/(x^2-3))^7 ?

The first derivative of y=((x^2+3)/(x^2-3))^7 is -(84x(x^2+3)^6)/((x^2-3)^8)

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derivative of

y = (\frac{x ^{2} + 3}{x ^{2} - 3})^{7}

- \frac{84 x ( x ^{2} + 3 ) ^{6}}{( x ^{2} - 3 ) ^{8}}

Solution steps

\frac{d}{d x} ((\frac{x ^{2} + 3}{x ^{2} - 3})^{7})

Apply the chain rule:

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

= 7 (\frac{x ^{2} + 3}{x ^{2} - 3})^{6} \frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3}) = - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

= 7 (\frac{x ^{2} + 3}{x ^{2} - 3})^{6} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

Simplify

7 (\frac{x ^{2} + 3}{x ^{2} - 3})^{6} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{84 x ( x ^{2} + 3 ) ^{6}}{( x ^{2} - 3 ) ^{8}}

= - \frac{84 x ( x ^{2} + 3 ) ^{6}}{( x ^{2} - 3 ) ^{8}}

x \to 2 lim (x^{2} + 5 x - 9)

y = 3 tan (3 t)

cot^{2} (cos (θ))

\frac{d}{d x} (arcsin (6 x^{4}))

\frac{d}{d x} (\frac{x ^{2}}{3} + \frac{5 x}{7} - \frac{8}{5})

What is the derivative of y=((x^2+3)/(x^2-3))^7 ?
The derivative of y=((x^2+3)/(x^2-3))^7 is -(84x(x^2+3)^6)/((x^2-3)^8)
What is the first derivative of y=((x^2+3)/(x^2-3))^7 ?
The first derivative of y=((x^2+3)/(x^2-3))^7 is -(84x(x^2+3)^6)/((x^2-3)^8)