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

The derivative of (4x/((3x^2-1)^2)) is (4(-1-9x^2))/((3x^2-1)^3)

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

The first derivative of (4x/((3x^2-1)^2)) is (4(-1-9x^2))/((3x^2-1)^3)

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

\frac{4 ( - 1 - 9 x ^{2} )}{( 3 x ^{2} - 1 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

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

\frac{d}{d x} ((3 x^{2} - 1)^{2}) = 12 x (3 x^{2} - 1)

= 4 \cdot \frac{1 \cdot ( 3 x ^{2} - 1 ) ^{2} - 12 x ( 3 x ^{2} - 1 ) x}{( ( 3 x ^{2} - 1 ) ^{2} ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( 3 x ^{2} - 1 ) ^{2} - 12 x ( 3 x ^{2} - 1 ) x}{( ( 3 x ^{2} - 1 ) ^{2} ) ^{2}} : \frac{4 ( - 1 - 9 x ^{2} )}{( 3 x ^{2} - 1 ) ^{3}}

= \frac{4 ( - 1 - 9 x ^{2} )}{( 3 x ^{2} - 1 ) ^{3}}

\int 4 x - 3 x^{2} d x

f (t) = t (sin (9 t) + e^{- 2 t})

\int_{0}^{π} sin^{2} (6 x) d x

\frac{\partial}{\partial x} (x (x + 3 y + 2))

\frac{d y}{d x} = 20 + 28 x + 40 y + 56 x y

What is the derivative of (4x/((3x^2-1)^2)) ?
The derivative of (4x/((3x^2-1)^2)) is (4(-1-9x^2))/((3x^2-1)^3)
What is the first derivative of (4x/((3x^2-1)^2)) ?
The first derivative of (4x/((3x^2-1)^2)) is (4(-1-9x^2))/((3x^2-1)^3)