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

The derivative of 2/((1-1/3 x^3+1^2)) is (108x^2)/((-x^3+6)^3)

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

The first derivative of 2/((1-1/3 x^3+1^2)) is (108x^2)/((-x^3+6)^3)

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

\frac{108 x ^{2}}{( - x ^{3} + 6 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 (- \frac{2}{( 1 - \frac{1}{3} x ^{3} + 1 ) ^{3}} (- x^{2})) : \frac{108 x ^{2}}{( - x ^{3} + 6 ) ^{3}}

= \frac{108 x ^{2}}{( - x ^{3} + 6 ) ^{3}}

5 x^{2} - 2 x - 1

\int \frac{x ^{2}}{x ^{4} + 10 x ^{2} + 9} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 x} ln (x)

f (x) = \frac{1}{7 - x}

\frac{d}{d x} (h (x))

What is the derivative of 2/((1-1/3 x^3+1^2)) ?
The derivative of 2/((1-1/3 x^3+1^2)) is (108x^2)/((-x^3+6)^3)
What is the first derivative of 2/((1-1/3 x^3+1^2)) ?
The first derivative of 2/((1-1/3 x^3+1^2)) is (108x^2)/((-x^3+6)^3)