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}}

\frac{\partial}{\partial x} (ln (x + y^{3} + x y^{2}))

\frac{\partial}{\partial z} (x^{2} y z^{2})

\frac{d}{d x} (1 - \frac{3}{x + 7})

\frac{d}{d x} (cos (e^{3 x}))

\int_{1}^{5} 2 x + 1 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)