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

The derivative of ((x+5/(x^2+2))^2) is (2(x+5)(-x^2-10x+2))/((x^2+2)^3)

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

The first derivative of ((x+5/(x^2+2))^2) is (2(x+5)(-x^2-10x+2))/((x^2+2)^3)

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

\frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{( x ^{2} + 2 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x + 5}{x ^{2} + 2}) = \frac{- x ^{2} - 10 x + 2}{( x ^{2} + 2 ) ^{2}}

= 2 \cdot \frac{x + 5}{x ^{2} + 2} \cdot \frac{- x ^{2} - 10 x + 2}{( x ^{2} + 2 ) ^{2}}

Simplify

2 \cdot \frac{x + 5}{x ^{2} + 2} \cdot \frac{- x ^{2} - 10 x + 2}{( x ^{2} + 2 ) ^{2}} : \frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{( x ^{2} + 2 ) ^{3}}

= \frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{( x ^{2} + 2 ) ^{3}}

\frac{d ^{2}}{d x ^{2}} (e^{\frac{6}{x}})

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

y = 0, y = 3 (x^{3} - x)

x \to 0 lim (cos (x))

- 6 x^{- 2}

What is the derivative of ((x+5/(x^2+2))^2) ?
The derivative of ((x+5/(x^2+2))^2) is (2(x+5)(-x^2-10x+2))/((x^2+2)^3)
What is the first derivative of ((x+5/(x^2+2))^2) ?
The first derivative of ((x+5/(x^2+2))^2) is (2(x+5)(-x^2-10x+2))/((x^2+2)^3)