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

The derivative of x/(sqrt(2-x^2)) is 2/((2-x^2)sqrt(2-x^2))

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

The first derivative of x/(sqrt(2-x^2)) is 2/((2-x^2)sqrt(2-x^2))

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

= \frac{2}{( 2 - x ^{2} ) 2 - x ^{2}}

f (x) = \frac{x}{x - 2}, at x = 3

(- 5.2) (2.5)

\frac{d}{d x} (sin (x + x) + 5)

\frac{\partial}{\partial x} (6 + x ln (x y - 9))

f (x) = x^{2} - 3 x + 2

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