What is the derivative of (12/((1-x)^5)) ?

The derivative of (12/((1-x)^5)) is (60)/((1-x)^6)

What is the first derivative of (12/((1-x)^5)) ?

The first derivative of (12/((1-x)^5)) is (60)/((1-x)^6)

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\frac{d}{d x} (\frac{12}{( 1 - x ) ^{5}})

\frac{60}{( 1 - x ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{12}{( 1 - x ) ^{5}})

Take the constant out:

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

= 12 \frac{d}{d x} (\frac{1}{( 1 - x ) ^{5}})

Apply exponent rule:

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

= 12 \frac{d}{d x} ((1 - x)^{- 5})

Apply the chain rule:

- \frac{5}{( 1 - x ) ^{6}} \frac{d}{d x} (1 - x)

= - \frac{5}{( 1 - x ) ^{6}} \frac{d}{d x} (1 - x)

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

= 12 (- \frac{5}{( 1 - x ) ^{6}} (- 1))

Simplify

12 (- \frac{5}{( 1 - x ) ^{6}} (- 1)) : \frac{60}{( 1 - x ) ^{6}}

= \frac{60}{( 1 - x ) ^{6}}

n = 3 \sum \infty \frac{x ^{n}}{n !}

\int \frac{1}{1 - 49 x ^{2}} d x

\int \frac{x ^{2} - 25}{x - 5} d x

\frac{\partial}{\partial y} (4 x^{3} y^{3})

y = 2 x^{2} - 1, (0, 1)

What is the derivative of (12/((1-x)^5)) ?
The derivative of (12/((1-x)^5)) is (60)/((1-x)^6)
What is the first derivative of (12/((1-x)^5)) ?
The first derivative of (12/((1-x)^5)) is (60)/((1-x)^6)