In Exercises 17-26, calculate the derivative indicated. d* ff(t) = 6r° – 215dr4=1

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

In Exercises 17-26, calculate the derivative indicated.

Expert Solution

Step 1

Given that,

$f (t) = 6 t^{9} - 2 t^{5}$ ...(1)

Step 2

Differentiate f(t) with respect to t,

$\frac{d f}{d t} = \frac{d}{d t} (6 t^{9} - 2 t^{5}) \frac{d f}{d t} = 54 t^{8} - 10 t^{4} [U \sin g \frac{d}{d x} x^{n} = n x^{n - 1}] \frac{d f}{d t} = 54 t^{8} - 10 t^{4} . . . (2)$

Now differentiate (2) with respect to t,

$\frac{d^{2} f}{d t^{2}} = \frac{d}{d t} (54 t^{8} - 10 t^{4}) \frac{d^{2} f}{d t^{2}} = 432 t^{7} - 40 t^{3} . . . (3)$

Again differentiate (3) with respect to t,

$\frac{d^{3} f}{d t^{3}} = \frac{d}{d t} (432 t^{7} - 40 t^{3}) \frac{d^{3} f}{d t^{3}} = 3024 t^{6} - 120 t^{2} A n d \frac{d^{4} f}{d t^{4}} = \frac{d}{d t} (3024 t^{6} - 120 t^{2}) \frac{d^{4} f}{d t^{4}} = 18144 t^{5} - 240 t . . . (4)$