Differentiate each expression.

Question

Here are some examples of questions in the textbook that I don't know how to do for my test!

Differentiate each expression:

 

y=xcosx

 

 

y=sec^2xcotx

 

 

y=sin^2(tan(x^2-3))

 

 

y=sec^2x-tan^2x

Answer 1

Let's try:

y = sin[tan(x² - 3)]²

y' = 2[sin(tan(x² - 3))]¹ • cos[tan(x² - 3)] • sec²(x² - 3) • 2x

= 4x • sin[tan(x² - 3)] • cos[tan(x² - 3)] • sec²(x² - 3)

The chain rule was used 3 times.

1. Derivative of sin[tan(x² - 3)] = cos[tan(x² - 3)]
2. Derivative of tan(x² - 3) = sec²(x² - 3)
3. Derivative of x² - 3 = 2x