Calculus Derivatives and Functions

This tutorial guides users on how to determine derivatives using the TI-89 graphing calculator. It covers accessing the calculus menu, entering functions and variables, and using the home screen for derivative calculations. The video also explains handling trigonometric functions and applying the quotient rule for derivatives. Each step is demonstrated with examples, ensuring a comprehensive understanding of using the TI-89 for calculus operations.

What is the first step to access the derivative function on the TA 89 graphing calculator?

• Press F5

• Press F3

• Press F1

• Press F2

When entering a fraction in a function, what is crucial to ensure the correct part is in the denominator?

• Use a comma

• Use a colon

• Use a semicolon

• Use parentheses

What is the derivative of the function f(x) = 2x^3 - 5/(2x^2) + ln(x) + 7x^(2/3)?

• 6x^2 + 14/3x^(1/3) + 1x + 5/x^3

• 6x^2 + 14/3x^(1/3) + 1/x + 5/x^3

• 6x^2 + 14/3x^(1/3) + 1x + 5x^3

• 6x^2 + 14/3x^(1/3) + 1x + 5/x^2

How can you access the derivative function from the home screen on the TA 89?

• Press second 6

• Press second 7

• Press second 9

• Press second 8

What is the derivative of the function G(T) = -3(2T^5 - 8)^4?

• 960T^4 * (T^5 - 8)^4

• 960T^4 * (T^5 - 8)^3

• 960T^4 * (T^5 - 4)^3

• 960T^5 * (T^5 - 4)^3

What is the correct way to enter a trigonometric function raised to a power on the TA 89?

• Enter the function without any special format

• Use a comma after the function

• Use parentheses around the function

• Enter the power first

What is the derivative of the function H(x) = 3(tan(x^3))^2?

• 6x^2 * sec(x^3) * tan(x^3)

• 6x^2 * sec^2(x^3)

• 6x^3 * sec^2(x^3) * tan(x^3)

• 6x^2 * sec^2(x^3) * tan(x^3)

What should you do to ensure both the numerator and denominator are correctly entered in a rational function?

• Use a comma between them

• Use parentheses around each

• Use a semicolon between them

• Use a colon between them

What is the derivative of the function J(x) = (4x^3 - e^x) / (3x^2 - 1)?

• (12x^2 - e^x) / (3x^2 - 1)^2

• (12x^2 - e^x) / (3x^2 - 1)

• (12x^2 - e^x) / (3x^2 + 1)

• (12x^2 + e^x) / (3x^2 - 1)^2

What should you do if the derivative function result is too long to view on the screen?

• Press the up arrow

• Press the right arrow

• Press the left arrow

• Press the down arrow