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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{x ^{n}}{n !})

\int_{0}^{π} sin^{4} (2 x) d x

x \to - \infty lim (x \cdot e^{x})

\frac{d}{d y} (sin^{2} (y))

\int_{- 10}^{10} π (100 - x^{2}) d x

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