Calculating Derivatives and Inverse Functions

The video tutorial explains how to find the derivative of a function using the product rule. It involves differentiating the function f(x) = 2x^7 * inverse hyperbolic sine of 5x. The process includes applying the product rule, differentiating the inverse hyperbolic sine function, and simplifying the expression. The tutorial also demonstrates how to calculate f prime of 1 by substituting x=1 and evaluates the result using calculators like the T84 and Desmos. The video concludes with a summary of the steps and results.

What is the first step in finding the derivative of the given function?

• Use integration by parts

• Differentiate directly

• Use the product rule

• Apply the chain rule

Which function is considered the 'first function' in the product rule application?

• Inverse hyperbolic sine of 5x

• 2x to the 7th

• 5x

• 14x to the 6th

What is the derivative of the inverse hyperbolic sine of 5x?

• 5 divided by the square root of 25x squared plus 1

• 1 divided by the square root of 25x squared plus 1

• 5 times the square root of 25x squared plus 1

• 1 times the square root of 25x squared plus 1

How is f'(1) calculated after finding f'(x)?

• By substituting x = 7

• By substituting x = 1

• By substituting x = 0

• By substituting x = 5

What is the exact value of f'(1) before using a calculator?

• 10 divided by the square root of 26 plus 14 times inverse hyperbolic sine of 5

• 10 divided by the square root of 25 plus 1 plus 14 times inverse hyperbolic sine of 5

• 10 times the square root of 26 plus 14 times inverse hyperbolic sine of 5

• 10 times the square root of 25 plus 1 plus 14 times inverse hyperbolic sine of 5

Which button is used to access the inverse hyperbolic sine function on the T84 calculator?

• Second x squared

• Second S

• Second log

• Second zero

What is the approximate value of f'(1) to four decimal places?

• 35.3353

• 33.4353

• 34.3353

• 32.3353

What is the main advantage of using the Desmos calculator for evaluating the derivative?

• It is easier to use

• It is more accurate

• It is faster

• It provides step-by-step solutions

What is the first step in using the Desmos calculator to evaluate the derivative?

• Calculate the square of 5x

• Enter the square root function

• Press the inverse hyperbolic sine button

• Type in the derivative function value

What is the final step in evaluating the derivative using the Desmos calculator?

• Multiply by 14

• Calculate the square root

• Type the inverse hyperbolic sine function

• Press enter