What is the derivative of (30/((1-x)^4)) ?

The derivative of (30/((1-x)^4)) is (120)/((1-x)^5)

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

The first derivative of (30/((1-x)^4)) is (120)/((1-x)^5)

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

\frac{120}{( 1 - x ) ^{5}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= 30 \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

= 30 (- \frac{4}{( 1 - x ) ^{5}} (- 1))

Simplify

30 (- \frac{4}{( 1 - x ) ^{5}} (- 1)) : \frac{120}{( 1 - x ) ^{5}}

= \frac{120}{( 1 - x ) ^{5}}

y^{^{'''}} + 4 y^{^{''}} - 6 y^{^{'}} - 12 y = 0

5 y^{^{''}} + y^{^{'}} = - 2 x

\frac{2}{s} + \frac{3}{s + 1}

\frac{d}{d x} (\frac{( 4 x ^{2} + 6 x + 4 )}{x})

\frac{( e ^{t} )}{1 + t}

What is the derivative of (30/((1-x)^4)) ?
The derivative of (30/((1-x)^4)) is (120)/((1-x)^5)
What is the first derivative of (30/((1-x)^4)) ?
The first derivative of (30/((1-x)^4)) is (120)/((1-x)^5)