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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int \frac{( 3 x + 2 )}{x ( x + 1 ) ^{2}} d x

2 e^{- x}

\int \frac{sec ^{2} ( x )}{tan ^{3} ( x )} d x

6 t \frac{d y}{d t} + y = t

3 x^{2} - 3

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