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Popular >

derivative of 2(1-x^{-3})

Solution

\frac{d}{d x} (2 (1 - x)^{- 3})

Solution

\frac{6}{( 1 - x ) ^{4}}

Solution steps

\frac{d}{d x} (2 (1 - x)^{- 3})

Take the constant out:

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

= 2 \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

= 2 (- \frac{3}{( 1 - x ) ^{4}} (- 1))

Simplify

2 (- \frac{3}{( 1 - x ) ^{4}} (- 1)) : \frac{6}{( 1 - x ) ^{4}}

= \frac{6}{( 1 - x ) ^{4}}

Popular Examples

limit as x approaches 0 of (5^x-4^x)/x

x \to 0 lim (\frac{5 ^{x} - 4 ^{x}}{x})

derivative of (2x+3)/(3x+2)derivative of

\frac{2 x + 3}{3 x + 2}

integral from 0 to 1 of z/((z^2+1)^3)

\int_{0}^{1} \frac{z}{( z ^{2} + 1 ) ^{3}} d z

limit as x approaches 0+of ln(x^3)

x \to 0 + lim (ln (x^{3}))

(1+t^2)y^'+4ty=t

(1 + t^{2}) y^{^{'}} + 4 t y = t

Frequently Asked Questions (FAQ)

What is the derivative of 2(1-x^{-3}) ?
The derivative of 2(1-x^{-3}) is 6/((1-x)^4)
What is the first derivative of 2(1-x^{-3}) ?
The first derivative of 2(1-x^{-3}) is 6/((1-x)^4)