What is the derivative of (x/(2(x^2-1^2-1))^2) ?

The derivative of (x/(2(x^2-1^2-1))^2) is (2x(-6x^4+4x^2+1))/((2x^4-4x^2+1)^3)

What is the first derivative of (x/(2(x^2-1^2-1))^2) ?

The first derivative of (x/(2(x^2-1^2-1))^2) is (2x(-6x^4+4x^2+1))/((2x^4-4x^2+1)^3)

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\frac{d}{d x} (\frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1})^{2}

\frac{2 x ( - 6 x ^{4} + 4 x ^{2} + 1 )}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1})^{2}

Apply the chain rule:

2 \cdot \frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1} \frac{d}{d x} (\frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1})

= 2 \cdot \frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1} \frac{d}{d x} (\frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1})

\frac{d}{d x} (\frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1}) = \frac{- 6 x ^{4} + 4 x ^{2} + 1}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{2}}

= 2 \cdot \frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1} \cdot \frac{- 6 x ^{4} + 4 x ^{2} + 1}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{2}}

Simplify

2 \cdot \frac{x}{2 ( x ^{2} - 1 ) ^{2} - 1} \cdot \frac{- 6 x ^{4} + 4 x ^{2} + 1}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{2}} : \frac{2 x ( - 6 x ^{4} + 4 x ^{2} + 1 )}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{3}}

= \frac{2 x ( - 6 x ^{4} + 4 x ^{2} + 1 )}{( 2 x ^{4} - 4 x ^{2} + 1 ) ^{3}}

y^{^{''}} - 9 y = 0, y (0) = 6

x \to 54 lim (\frac{x ^{2}}{6} - \frac{9}{x})

x \to 2 lim (5 x^{2} - 2 x + 3)

\int \frac{1}{49 - x ^{2}} d x

What is the derivative of (x/(2(x^2-1^2-1))^2) ?
The derivative of (x/(2(x^2-1^2-1))^2) is (2x(-6x^4+4x^2+1))/((2x^4-4x^2+1)^3)
What is the first derivative of (x/(2(x^2-1^2-1))^2) ?
The first derivative of (x/(2(x^2-1^2-1))^2) is (2x(-6x^4+4x^2+1))/((2x^4-4x^2+1)^3)