What is the derivative of (4x/((1-x^2)^2)) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

e^{- 2 t} cos (2 t)

f (x) = 7 x^{3}

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

\int sin^{2} (6 x) cos^{2} (6 x) d x

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