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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 \frac{x ^{2} - 2}{x ^{2} + 2}} \cdot \frac{8 x}{( x ^{2} + 2 ) ^{2}}

Simplify

\frac{1}{2 \frac{x ^{2} - 2}{x ^{2} + 2}} \cdot \frac{8 x}{( x ^{2} + 2 ) ^{2}} : \frac{4 x}{x ^{2} - 2 ( x ^{2} + 2 ) ^{\frac{3}{2}}}

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

\frac{\partial}{\partial x} (6 e^{x^{3} y^{2}})

5 x^{2} + 5 x + 2

\int x^{\frac{3}{2}} (x^{2} + 3) (x + 2) d x

y^{^{'''}} + y^{^{''}} - 2 y = 0

x \to 3 lim (\frac{4 x ^{2} - 36}{2 x - 6})

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