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

The derivative of ((x^2/(x^2+2))^2) is (8x^3)/((x^2+2)^3)

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

The first derivative of ((x^2/(x^2+2))^2) is (8x^3)/((x^2+2)^3)

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

\frac{8 x ^{3}}{( x ^{2} + 2 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot \frac{x ^{2}}{x ^{2} + 2} \cdot \frac{4 x}{( x ^{2} + 2 ) ^{2}} : \frac{8 x ^{3}}{( x ^{2} + 2 ) ^{3}}

= \frac{8 x ^{3}}{( x ^{2} + 2 ) ^{3}}

cos (3 t + 5) e^{2 t}

\frac{d ^{2}}{d x ^{2}} (4 x - 5 x^{\frac{3}{4}})

\int - 4 sin (3 x) sin (n x) d x

\int x^{11} cos (x^{6}) d x

x \to 0 lim (x^{4} cos (\frac{2}{x}))

What is the derivative of ((x^2/(x^2+2))^2) ?
The derivative of ((x^2/(x^2+2))^2) is (8x^3)/((x^2+2)^3)
What is the first derivative of ((x^2/(x^2+2))^2) ?
The first derivative of ((x^2/(x^2+2))^2) is (8x^3)/((x^2+2)^3)