What is the derivative of (-1+2t)^{-1} ?

The derivative of (-1+2t)^{-1} is -2/((-1+2t)^2)

What is the first derivative of (-1+2t)^{-1} ?

The first derivative of (-1+2t)^{-1} is -2/((-1+2t)^2)

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derivative of

(- 1 + 2 t)^{- 1}

- \frac{2}{( - 1 + 2 t ) ^{2}}

Solution steps

\frac{d}{d t} ((- 1 + 2 t)^{- 1})

Apply the chain rule:

- \frac{1}{( - 1 + 2 t ) ^{2}} \frac{d}{d t} (- 1 + 2 t)

= - \frac{1}{( - 1 + 2 t ) ^{2}} \frac{d}{d t} (- 1 + 2 t)

\frac{d}{d t} (- 1 + 2 t) = 2

= - \frac{1}{( - 1 + 2 t ) ^{2}} \cdot 2

Simplify

- \frac{1}{( - 1 + 2 t ) ^{2}} \cdot 2 : - \frac{2}{( - 1 + 2 t ) ^{2}}

= - \frac{2}{( - 1 + 2 t ) ^{2}}

y = x^{3} + 2 x - 1

a^{\frac{1}{x}}

3 ln (2 x - 1)

\frac{( 3 x ^{2} + 5 ) ^{1}}{x}

y = x^{2} ln (4 x)

What is the derivative of (-1+2t)^{-1} ?
The derivative of (-1+2t)^{-1} is -2/((-1+2t)^2)
What is the first derivative of (-1+2t)^{-1} ?
The first derivative of (-1+2t)^{-1} is -2/((-1+2t)^2)