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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (1 + 3 x^{2}) = 6 x

= \frac{( 1 - 2 x ) ( 1 + 3 x ^{2} ) - 6 x ( x - x ^{2} )}{( 1 + 3 x ^{2} ) ^{2}}

Expand

(1 - 2 x) (1 + 3 x^{2}) - 6 x (x - x^{2}) : - 3 x^{2} - 2 x + 1

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

\frac{d}{d x} (ln (x))

f (x) = (3 x - 1) e^{- 6 x}

\frac{y + 1}{y - 1}

x \to \infty lim (1^{x})

\frac{d}{d x} (3 x + 16)

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