What is the derivative of (48)/((1-x)^4) ?

The derivative of (48)/((1-x)^4) is (192)/((1-x)^5)

What is the first derivative of (48)/((1-x)^4) ?

The first derivative of (48)/((1-x)^4) is (192)/((1-x)^5)

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derivative of

\frac{48}{( 1 - x ) ^{4}}

\frac{192}{( 1 - x ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{48}{( 1 - x ) ^{4}})

Take the constant out:

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

= 48 \frac{d}{d x} (\frac{1}{( 1 - x ) ^{4}})

Apply exponent rule:

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

= 48 \frac{d}{d x} ((1 - x)^{- 4})

Apply the chain rule:

- \frac{4}{( 1 - x ) ^{5}} \frac{d}{d x} (1 - x)

= - \frac{4}{( 1 - x ) ^{5}} \frac{d}{d x} (1 - x)

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

= 48 (- \frac{4}{( 1 - x ) ^{5}} (- 1))

Simplify

48 (- \frac{4}{( 1 - x ) ^{5}} (- 1)) : \frac{192}{( 1 - x ) ^{5}}

= \frac{192}{( 1 - x ) ^{5}}

What is the derivative of (48)/((1-x)^4) ?
The derivative of (48)/((1-x)^4) is (192)/((1-x)^5)
What is the first derivative of (48)/((1-x)^4) ?
The first derivative of (48)/((1-x)^4) is (192)/((1-x)^5)