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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

f (x) = \frac{sin ( π - x )}{π - x}

x \to 0 lim (5^{x + h} - 5^{x})

y^{^{'}} - tan (x) = 0

x - y

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