What is the derivative of (120/((1-x)^6)) ?

The derivative of (120/((1-x)^6)) is (720)/((1-x)^7)

What is the first derivative of (120/((1-x)^6)) ?

The first derivative of (120/((1-x)^6)) is (720)/((1-x)^7)

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\frac{d}{d x} (\frac{120}{( 1 - x ) ^{6}})

\frac{720}{( 1 - x ) ^{7}}

Solution steps

\frac{d}{d x} (\frac{120}{( 1 - x ) ^{6}})

Take the constant out:

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

= 120 \frac{d}{d x} (\frac{1}{( 1 - x ) ^{6}})

Apply exponent rule:

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

= 120 \frac{d}{d x} ((1 - x)^{- 6})

Apply the chain rule:

- \frac{6}{( 1 - x ) ^{7}} \frac{d}{d x} (1 - x)

= - \frac{6}{( 1 - x ) ^{7}} \frac{d}{d x} (1 - x)

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

= 120 (- \frac{6}{( 1 - x ) ^{7}} (- 1))

Simplify

120 (- \frac{6}{( 1 - x ) ^{7}} (- 1)) : \frac{720}{( 1 - x ) ^{7}}

= \frac{720}{( 1 - x ) ^{7}}

What is the derivative of (120/((1-x)^6)) ?
The derivative of (120/((1-x)^6)) is (720)/((1-x)^7)
What is the first derivative of (120/((1-x)^6)) ?
The first derivative of (120/((1-x)^6)) is (720)/((1-x)^7)