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Popular >

derivative of 1/(1-x^3)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 7 of 9

x \to 7 lim (9)

integral of 1/((1+t^2))

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

derivative of e^x(cos(x+sin(x)))

\frac{d}{d x} (e^{x} (cos (x) + sin (x)))

y^{''}+4y^'+4y=5cos(4x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 5 cos (4 x)

derivative of f(x)=5x^{2/3}-2x^3 derivative of

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

Frequently Asked Questions (FAQ)

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