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

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

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

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

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

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

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 (1 - 2 x)

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

Simplify

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

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

\int (cos (x))^{5} sin (x) d x

\int (x^{2} + 2 x)^{5} (2 x + 2) d x

\frac{d}{d x} (x^{5} e^{- x})

\frac{d}{d x} (\frac{3 x + 5}{x ^{2} - x})

\int \frac{5}{x ln ( 6 x )} d x

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