What is the derivative of ((x^2+3/(x^2-3))^4) ?

The derivative of ((x^2+3/(x^2-3))^4) is -(48x(x^2+3)^3)/((x^2-3)^5)

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

The first derivative of ((x^2+3/(x^2-3))^4) is -(48x(x^2+3)^3)/((x^2-3)^5)

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

- \frac{48 x ( x ^{2} + 3 ) ^{3}}{( x ^{2} - 3 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

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

Simplify

4 (\frac{x ^{2} + 3}{x ^{2} - 3})^{3} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{48 x ( x ^{2} + 3 ) ^{3}}{( x ^{2} - 3 ) ^{5}}

= - \frac{48 x ( x ^{2} + 3 ) ^{3}}{( x ^{2} - 3 ) ^{5}}

\frac{\partial}{\partial x} (\frac{x}{A})

\frac{d}{d x} (a cos^{3} (t))

n \to \infty lim (n - \frac{1}{n})

\int \frac{x}{x + 9} d x

\int 37 tan^{5} (x) sec^{4} (x) d x

What is the derivative of ((x^2+3/(x^2-3))^4) ?
The derivative of ((x^2+3/(x^2-3))^4) is -(48x(x^2+3)^3)/((x^2-3)^5)
What is the first derivative of ((x^2+3/(x^2-3))^4) ?
The first derivative of ((x^2+3/(x^2-3))^4) is -(48x(x^2+3)^3)/((x^2-3)^5)