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

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

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

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

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derivative of

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

- \frac{2 ( - x ^{4} + 3 x ^{2} )}{( x ^{2} + 1 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = (x^{2} + 1)^{- 2}

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

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

\frac{d}{d x} ((x^{2} + 1)^{- 2}) = - \frac{4 x}{( x ^{2} + 1 ) ^{3}}

= - 2 (3 x^{2} (x^{2} + 1)^{- 2} + (- \frac{4 x}{( x ^{2} + 1 ) ^{3}}) x^{3})

Simplify

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

= - \frac{2 ( - x ^{4} + 3 x ^{2} )}{( x ^{2} + 1 ) ^{3}}

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

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

\frac{\partial}{\partial x} (2 x y^{7} + x^{8} y^{7})

f (x) = x^{2} + 9

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

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