Problem

Find the first, second, and third derivatives of …

Problem 6 Easy Difficulty

Find the first, second, and third derivatives of the given functions.
$$s=8 t^{5}+5 t^{4}$$

Answer

960

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 23

The Derivative

Section 9

Higher Derivatives

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Video Transcript

And this problem, we need to recommend the full 2nd and 3rd derivative of the given function, which is S. Is equal to 80 to the power five plus five T. To the power four. So the first derivative will be D S D. T. That would be the derivative of 82. The power five plus five T. To the power for. So that will be eight times the derivative of T. To the power five, which is five T. To the power four plus five times the derivative of T. To the power for which is 40 Q. So we have 40 84 plus 20 T. Q. That is determined the second derivative. So that will be the derivative of this expression over here. So this will be equal to 40 times 40 Q plus 20 times three T square. So this will be equal to 160 T. Plus 60 d. Square. Let us determine the 3rd derivative. That will be the derivative of this expression. So this will be equal to 160 times three t square plus 60 times the derivative of two square t square, which is two T. So this will be equal to 4 80 t square Plus 120 T. So the positive negative is 42 to the power four plus 20 p. Q. The second derivative is 1 60 tQ 60 square, and the third derivative is for 80 p square plus 120 p. Yeah.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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