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

The derivative of-1/(t^3) is 3/(t^4)

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

The first derivative of-1/(t^3) is 3/(t^4)

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derivative of

- \frac{1}{t ^{3}}

\frac{3}{t ^{4}}

Solution steps

\frac{d}{d t} (- \frac{1}{t ^{3}})

Take the constant out:

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

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

Apply exponent rule:

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

= - \frac{d}{d t} (t^{- 3})

Apply the Power Rule:

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

= - (- 3 t^{- 3 - 1})

Simplify

- (- 3 t^{- 3 - 1}) : \frac{3}{t ^{4}}

= \frac{3}{t ^{4}}

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