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

The derivative of (2-x^2/(3x^2+1)) is -(14x)/((3x^2+1)^2)

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

The first derivative of (2-x^2/(3x^2+1)) is -(14x)/((3x^2+1)^2)

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

- \frac{14 x}{( 3 x ^{2} + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 2 x ) ( 3 x ^{2} + 1 ) - 6 x ( 2 - x ^{2} )}{( 3 x ^{2} + 1 ) ^{2}} : - \frac{14 x}{( 3 x ^{2} + 1 ) ^{2}}

= - \frac{14 x}{( 3 x ^{2} + 1 ) ^{2}}

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

\frac{d}{d x} (x^{2} \cdot x^{7})

\frac{\partial}{\partial y} (x^{4} y^{2} - x^{3} y)

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

f (x) = \frac{e ^{x}}{4 - 4 x}

What is the derivative of (2-x^2/(3x^2+1)) ?
The derivative of (2-x^2/(3x^2+1)) is -(14x)/((3x^2+1)^2)
What is the first derivative of (2-x^2/(3x^2+1)) ?
The first derivative of (2-x^2/(3x^2+1)) is -(14x)/((3x^2+1)^2)