What is the derivative of 6/((1-x^3)) ?

The derivative of 6/((1-x^3)) is (18)/((1-x)^4)

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

The first derivative of 6/((1-x^3)) is (18)/((1-x)^4)

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

\frac{18}{( 1 - x ) ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= 6 (- \frac{3}{( 1 - x ) ^{4}} (- 1))

Simplify

6 (- \frac{3}{( 1 - x ) ^{4}} (- 1)) : \frac{18}{( 1 - x ) ^{4}}

= \frac{18}{( 1 - x ) ^{4}}

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 3 z^{2})

y = 10 x, y = x^{2} - 11

\int x (2 x + 1) d x

\frac{\partial}{\partial y} (m sin (2 (m x + n y)))

y = \frac{1}{3 t}, (2, \frac{1}{6})

What is the derivative of 6/((1-x^3)) ?
The derivative of 6/((1-x^3)) is (18)/((1-x)^4)
What is the first derivative of 6/((1-x^3)) ?
The first derivative of 6/((1-x^3)) is (18)/((1-x)^4)