Resolved: "Find the derivatives of the functions f(t)=t2−1t2+t−2" - Plainmath

Tazmin Horton

Answered question

2021-02-21

Find the derivatives of the functions

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

Answer & Explanation

Nola Robson

Skilled2021-02-23Added 94 answers

Step 1
We write f(t) using exponents first, then find the derivatives using the power rule.

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

f (t) = t^{2} - t^{- 2} + t - 2

f^{(1)} (t) = 2 t - (- 2) t^{- 3} + 1 - 0

f^{(1)} = 2 t + 2 t^{- 3} + 1

f^{(2)} (t) = 2 (1) + 2 (- 3) t^{- 4} + 0

f^{(2)} (t) = 2 - 6 t^{- 4}

Step 2

f^{(2)} (t) = 2 - 6 t^{- 4}

f^{(3)} (t) = - 6 (- 4) t^{- 5}

f^{(3)} (t) = 24 t^{- 5}

f^{(4)} (t) = - 120 t^{- 6}

Then we generalize the next derivatives

f^{(n)} (t) = {(- 1)}^{n + 1} (n + 1)! (t^{- 6})

for integer n > 2

Jeffrey Jordon

Expert2022-03-24Added 2605 answers

Answer is given below (on video)

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