What is the derivative of (24/((1-x)^4)) ?

The derivative of (24/((1-x)^4)) is (96)/((1-x)^5)

What is the first derivative of (24/((1-x)^4)) ?

The first derivative of (24/((1-x)^4)) is (96)/((1-x)^5)

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\frac{d}{d x} (\frac{24}{( 1 - x ) ^{4}})

\frac{96}{( 1 - x ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{24}{( 1 - x ) ^{4}})

Take the constant out:

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

= 24 \frac{d}{d x} (\frac{1}{( 1 - x ) ^{4}})

Apply exponent rule:

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

= 24 \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

= 24 (- \frac{4}{( 1 - x ) ^{5}} (- 1))

Simplify

24 (- \frac{4}{( 1 - x ) ^{5}} (- 1)) : \frac{96}{( 1 - x ) ^{5}}

= \frac{96}{( 1 - x ) ^{5}}

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

\frac{4}{5 x + 1}, at x = - 1

x \to 3 lim (3 - x)

x \to \infty lim (8 x)

x y^{^{'}} + 2 y = \frac{2}{x ^{2}} + 1

What is the derivative of (24/((1-x)^4)) ?
The derivative of (24/((1-x)^4)) is (96)/((1-x)^5)
What is the first derivative of (24/((1-x)^4)) ?
The first derivative of (24/((1-x)^4)) is (96)/((1-x)^5)