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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

(cos^{4} (x))^{^{'}}

x \to 0 lim (\frac{sin ( - 4 x )}{x})

\int \frac{x ^{6}}{x ^{14} - 9} d x

4 + 3 x

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

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