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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d t} (e^{- a t} cos (x t))

y^{^{'}} = \frac{2 x ^{5} e ^{\frac{y}{x}} + x ^{3} y ^{2}}{x ^{4} y}

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

\frac{\partial}{\partial x} (x + 3 y)

(lo g_{e} (x))^{^{'}}

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