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

The derivative of y=(((x^2-2)/(2x^2+1))^2) is (20x(x^2-2))/((2x^2+1)^3)

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

The first derivative of y=(((x^2-2)/(2x^2+1))^2) is (20x(x^2-2))/((2x^2+1)^3)

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derivative of

y = ((\frac{x ^{2} - 2}{2 x ^{2} + 1})^{2})

\frac{20 x ( x ^{2} - 2 )}{( 2 x ^{2} + 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} - 2}{2 x ^{2} + 1}) = \frac{10 x}{( 2 x ^{2} + 1 ) ^{2}}

= 2 \cdot \frac{x ^{2} - 2}{2 x ^{2} + 1} \cdot \frac{10 x}{( 2 x ^{2} + 1 ) ^{2}}

Simplify

2 \cdot \frac{x ^{2} - 2}{2 x ^{2} + 1} \cdot \frac{10 x}{( 2 x ^{2} + 1 ) ^{2}} : \frac{20 x ( x ^{2} - 2 )}{( 2 x ^{2} + 1 ) ^{3}}

= \frac{20 x ( x ^{2} - 2 )}{( 2 x ^{2} + 1 ) ^{3}}

\int 6 d x

\frac{d}{d x} (∣ 2 x - 1 ∣)

\frac{\partial}{\partial x} (\frac{( x - y )}{x + y})

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

y^{^{'}} + 3 y = 4 e^{- t}

What is the derivative of y=(((x^2-2)/(2x^2+1))^2) ?
The derivative of y=(((x^2-2)/(2x^2+1))^2) is (20x(x^2-2))/((2x^2+1)^3)
What is the first derivative of y=(((x^2-2)/(2x^2+1))^2) ?
The first derivative of y=(((x^2-2)/(2x^2+1))^2) is (20x(x^2-2))/((2x^2+1)^3)