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

The derivative of f(x)= 1/((3x^2-1)^2) is -(12x)/((3x^2-1)^3)

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

The first derivative of f(x)= 1/((3x^2-1)^2) is -(12x)/((3x^2-1)^3)

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} - 1) = 6 x

= - \frac{2}{( 3 x ^{2} - 1 ) ^{3}} \cdot 6 x

Simplify

- \frac{2}{( 3 x ^{2} - 1 ) ^{3}} \cdot 6 x : - \frac{12 x}{( 3 x ^{2} - 1 ) ^{3}}

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

f (x) = x^{2} + 3, (3, 12)

\int (3 x^{2} tan (y) - \frac{2 y ^{3}}{x ^{3}}) d x

f (x) = 3 csc (4 x)

(y^{4} - x^{2}) d y + x y d x = 0

x^{2} - 5 x

What is the derivative of f(x)= 1/((3x^2-1)^2) ?
The derivative of f(x)= 1/((3x^2-1)^2) is -(12x)/((3x^2-1)^3)
What is the first derivative of f(x)= 1/((3x^2-1)^2) ?
The first derivative of f(x)= 1/((3x^2-1)^2) is -(12x)/((3x^2-1)^3)