What is the derivative of x= 1/t ?

The derivative of x= 1/t is -1/(t^2)

What is the first derivative of x= 1/t ?

The first derivative of x= 1/t is -1/(t^2)

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derivative of

x = \frac{1}{t}

- \frac{1}{t ^{2}}

Solution steps

\frac{d}{d t} (\frac{1}{t})

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 1 \cdot t^{- 1 - 1}

Simplify

- 1 \cdot t^{- 1 - 1} : - \frac{1}{t ^{2}}

= - \frac{1}{t ^{2}}

\frac{t ^{3}}{6}

\frac{1}{x ^{2} + y ^{2}}

y = x^{5} + x^{3} - x + 10

5 x^{2} + 3 x + 5

4 x^{2} - 5 x - 1

What is the derivative of x= 1/t ?
The derivative of x= 1/t is -1/(t^2)
What is the first derivative of x= 1/t ?
The first derivative of x= 1/t is -1/(t^2)