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

The derivative of (1+x^2/(1-x^2)) is (4x)/((1-x^2)^2)

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

The first derivative of (1+x^2/(1-x^2)) is (4x)/((1-x^2)^2)

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

\frac{4 x}{( 1 - x ^{2} ) ^{2}}

Solution steps

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

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

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

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

Simplify

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

= \frac{4 x}{( 1 - x ^{2} ) ^{2}}

\int_{1}^{2} \frac{11}{x ^{3} + 3 x} d x

\int \frac{1}{x ^{2} \cdot 9 + x ^{2}} d x

\int x (cos (x))^{2} d x

\int \frac{x}{25 + x ^{2}} d x

What is the derivative of (1+x^2/(1-x^2)) ?
The derivative of (1+x^2/(1-x^2)) is (4x)/((1-x^2)^2)
What is the first derivative of (1+x^2/(1-x^2)) ?
The first derivative of (1+x^2/(1-x^2)) is (4x)/((1-x^2)^2)