What is the derivative of (10/((1-x)^3)) ?

The derivative of (10/((1-x)^3)) is (30)/((1-x)^4)

What is the first derivative of (10/((1-x)^3)) ?

The first derivative of (10/((1-x)^3)) is (30)/((1-x)^4)

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\frac{d}{d x} (\frac{10}{( 1 - x ) ^{3}})

\frac{30}{( 1 - x ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{10}{( 1 - x ) ^{3}})

Take the constant out:

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

= 10 \frac{d}{d x} (\frac{1}{( 1 - x ) ^{3}})

Apply exponent rule:

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

= 10 \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

= 10 (- \frac{3}{( 1 - x ) ^{4}} (- 1))

Simplify

10 (- \frac{3}{( 1 - x ) ^{4}} (- 1)) : \frac{30}{( 1 - x ) ^{4}}

= \frac{30}{( 1 - x ) ^{4}}

\int (- \frac{6}{x ^{4}}) d x

\int \frac{2 x - 3}{( x ^{2} + 2 x - 3 ) ^{\frac{3}{2}}} d x

2^{t}

\int \frac{8 x - 2}{x ^{2} - 1} d x

\int e^{9 x} d x

What is the derivative of (10/((1-x)^3)) ?
The derivative of (10/((1-x)^3)) is (30)/((1-x)^4)
What is the first derivative of (10/((1-x)^3)) ?
The first derivative of (10/((1-x)^3)) is (30)/((1-x)^4)