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

The derivative of (1+2x^2/((1-2x^2)^2)) is (4x(2x^2+3))/((1-2x^2)^3)

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

The first derivative of (1+2x^2/((1-2x^2)^2)) is (4x(2x^2+3))/((1-2x^2)^3)

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

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

Solution steps

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

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

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

= \frac{4 x ( 1 - 2 x ^{2} ) ^{2} - ( - 8 x ( 1 - 2 x ^{2} ) ) ( 1 + 2 x ^{2} )}{( ( 1 - 2 x ^{2} ) ^{2} ) ^{2}}

Simplify

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

= \frac{4 x ( 2 x ^{2} + 3 )}{( 1 - 2 x ^{2} ) ^{3}}

\int x^{4} \cdot e^{- x^{5}} d x

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

f (x) = 5 x^{e}

y^{^{'}} = 1 - sin (y), y (0) = 0

\int_{- 1}^{1} 3 x^{2} (2 x^{3} + 1)^{2} d x

What is the derivative of (1+2x^2/((1-2x^2)^2)) ?
The derivative of (1+2x^2/((1-2x^2)^2)) is (4x(2x^2+3))/((1-2x^2)^3)
What is the first derivative of (1+2x^2/((1-2x^2)^2)) ?
The first derivative of (1+2x^2/((1-2x^2)^2)) is (4x(2x^2+3))/((1-2x^2)^3)