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

The derivative of (1+2x/(sqrt(1-x^2))) is (x+2)/((1-x^2)sqrt(1-x^2))

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

The first derivative of (1+2x/(sqrt(1-x^2))) is (x+2)/((1-x^2)sqrt(1-x^2))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{2 z}{x + y})

\frac{d}{d x} (\frac{2 x + 4 x ^{2}}{( 1 + 4 x ) ^{2}})

x \to - 5 - lim (\frac{x}{x + 5})

(50, 43), (60, 86)

\frac{d y}{d x} = - 10 x y^{2}

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