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

The derivative of-(2(-3x^2+1)/((x^2+1)^3)) is (24x(-x^2+1))/((x^2+1)^4)

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

The first derivative of-(2(-3x^2+1)/((x^2+1)^3)) is (24x(-x^2+1))/((x^2+1)^4)

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

\frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

- 2 \cdot \frac{( - 6 x ) ( x ^{2} + 1 ) ^{3} - 6 x ( x ^{2} + 1 ) ^{2} ( - 3 x ^{2} + 1 )}{( ( x ^{2} + 1 ) ^{3} ) ^{2}} : \frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

= \frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

f (x) = x^{3} - 4 x + 6, (2, 6)

f (x) = x^{2} (2 + x^{- 3})

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

\int \frac{14}{x ^{2} + 1} d x

\frac{d}{d x} (e^{f (x)})

What is the derivative of-(2(-3x^2+1)/((x^2+1)^3)) ?
The derivative of-(2(-3x^2+1)/((x^2+1)^3)) is (24x(-x^2+1))/((x^2+1)^4)
What is the first derivative of-(2(-3x^2+1)/((x^2+1)^3)) ?
The first derivative of-(2(-3x^2+1)/((x^2+1)^3)) is (24x(-x^2+1))/((x^2+1)^4)