What is the derivative of ((x^2+3/(x^2-3))^5) ?

The derivative of ((x^2+3/(x^2-3))^5) is -(60x(x^2+3)^4)/((x^2-3)^6)

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

The first derivative of ((x^2+3/(x^2-3))^5) is -(60x(x^2+3)^4)/((x^2-3)^6)

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

- \frac{60 x ( x ^{2} + 3 ) ^{4}}{( x ^{2} - 3 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

= 5 (\frac{x ^{2} + 3}{x ^{2} - 3})^{4} \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}}

= 5 (\frac{x ^{2} + 3}{x ^{2} - 3})^{4} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

Simplify

5 (\frac{x ^{2} + 3}{x ^{2} - 3})^{4} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{60 x ( x ^{2} + 3 ) ^{4}}{( x ^{2} - 3 ) ^{6}}

= - \frac{60 x ( x ^{2} + 3 ) ^{4}}{( x ^{2} - 3 ) ^{6}}

\int cos^{18} (x) sin (x) d x

- 5 (7 x^{2} + 4)^{- 6}

z \to 10 lim (\frac{1}{z - 10})

\int arccos (\frac{1}{x}) d x

y = 8 x^{2} - 2 x, y = x^{3} - 8 x + 3

What is the derivative of ((x^2+3/(x^2-3))^5) ?
The derivative of ((x^2+3/(x^2-3))^5) is -(60x(x^2+3)^4)/((x^2-3)^6)
What is the first derivative of ((x^2+3/(x^2-3))^5) ?
The first derivative of ((x^2+3/(x^2-3))^5) is -(60x(x^2+3)^4)/((x^2-3)^6)