What is the derivative of 1/(5-5x^3) ?

The derivative of 1/(5-5x^3) is (3x^2)/(5(x^3-1)^2)

What is the first derivative of 1/(5-5x^3) ?

The first derivative of 1/(5-5x^3) is (3x^2)/(5(x^3-1)^2)

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derivative of

\frac{1}{5 - 5 x ^{3}}

\frac{3 x ^{2}}{5 ( x ^{3} - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{5 - 5 x ^{3}})

Apply exponent rule:

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

= \frac{d}{d x} ((5 - 5 x^{3})^{- 1})

Apply the chain rule:

- \frac{1}{( 5 - 5 x ^{3} ) ^{2}} \frac{d}{d x} (5 - 5 x^{3})

= - \frac{1}{( 5 - 5 x ^{3} ) ^{2}} \frac{d}{d x} (5 - 5 x^{3})

\frac{d}{d x} (5 - 5 x^{3}) = - 15 x^{2}

= - \frac{1}{( 5 - 5 x ^{3} ) ^{2}} (- 15 x^{2})

Simplify

- \frac{1}{( 5 - 5 x ^{3} ) ^{2}} (- 15 x^{2}) : \frac{3 x ^{2}}{5 ( x ^{3} - 1 ) ^{2}}

= \frac{3 x ^{2}}{5 ( x ^{3} - 1 ) ^{2}}

\int 19 e^{x} d x

x \to 1 lim (x^{2} - 1)

\int e^{x} sin (x) x d x

\frac{s}{s ( s ^{2} + s + 1 )}

\int x cos^{2} (8 x) d x

What is the derivative of 1/(5-5x^3) ?
The derivative of 1/(5-5x^3) is (3x^2)/(5(x^3-1)^2)
What is the first derivative of 1/(5-5x^3) ?
The first derivative of 1/(5-5x^3) is (3x^2)/(5(x^3-1)^2)