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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x y - 2 y^{2} = 3

\frac{\partial}{\partial x} (6 y^{\frac{x}{z}})

sec (x) d y = x cot (y) d x

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

y = 0, y = x, [0, 1]

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