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

The derivative of ((x^2+4/(x^2-4))^5) is -(80x(x^2+4)^4)/((x^2-4)^6)

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

The first derivative of ((x^2+4/(x^2-4))^5) is -(80x(x^2+4)^4)/((x^2-4)^6)

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

- \frac{80 x ( x ^{2} + 4 ) ^{4}}{( x ^{2} - 4 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} + 4}{x ^{2} - 4}) = - \frac{16 x}{( x ^{2} - 4 ) ^{2}}

= 5 (\frac{x ^{2} + 4}{x ^{2} - 4})^{4} (- \frac{16 x}{( x ^{2} - 4 ) ^{2}})

Simplify

5 (\frac{x ^{2} + 4}{x ^{2} - 4})^{4} (- \frac{16 x}{( x ^{2} - 4 ) ^{2}}) : - \frac{80 x ( x ^{2} + 4 ) ^{4}}{( x ^{2} - 4 ) ^{6}}

= - \frac{80 x ( x ^{2} + 4 ) ^{4}}{( x ^{2} - 4 ) ^{6}}

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

\frac{d}{d x} (x^{s i n^{2} (x)})

\frac{d}{d a} (\frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}})

\frac{\partial}{\partial x} (5)

\frac{d y}{d x} - \frac{( y ^{2} - x ^{2} )}{3 x y} = 0

What is the derivative of ((x^2+4/(x^2-4))^5) ?
The derivative of ((x^2+4/(x^2-4))^5) is -(80x(x^2+4)^4)/((x^2-4)^6)
What is the first derivative of ((x^2+4/(x^2-4))^5) ?
The first derivative of ((x^2+4/(x^2-4))^5) is -(80x(x^2+4)^4)/((x^2-4)^6)