Learn how use the quotient rule to take the derivative including cosine

The video tutorial explains how to find the derivative of a function using the quotient rule. It begins by defining the function Y as cosine of X divided by cosine of X, and then identifies the numerator and denominator functions. The derivatives of these functions are calculated, and the quotient rule is applied to find the derivative of the entire function. The final result is presented as the derivative of Y with respect to X.

What is the derivative of FX if FX equals cosine of X?

• cosine of X

• negative sine of X

• sine of X

• negative cosine of X

What is the expression for G prime of X if G of X is X?

• negative X

• 0

• X

• 1

Which of the following is the correct setup for the quotient rule?

• F prime of X times G of X minus F of X times G prime of X

• F of X times G of X minus F prime of X times G prime of X

• G prime of X times F of X minus G of X times F prime of X

• F prime of X times G prime of X minus F of X times G of X

What is the result of applying the quotient rule to find Dy DX?

• X sine of X minus cosine of X all over X squared

• negative X sine of X plus cosine of X all over X squared

• X sine of X plus cosine of X all over X squared

• negative X sine of X minus cosine of X all over X squared

What is the denominator in the final expression for Dy DX?

• X

• X squared

• sine of X

• cosine of X