11.
Recall that (tan x) = sec^2 x and that (sec x) = sec x tan x. Using the Quotient Rule, we get
= . This can be simplified (using trigonometric identities)
to .
12.
Recall that (cot x) = −csc^2 x. Here we use the Chain Rule to find the derivative: =
= .
SOLUTIONS TO PRACTICE PROBLEM SET 7
1.
We take the derivative of each term with respect to x: (3x^2 ) − (3y^2 ) = (1).
Next, because = 1, we can eliminate that term and get (3x^2 ) − (3y^2 ) = .
Next, group the terms containing :(3x^2 ) = + (3y^2 ).
Factor out the term : (3x^2 ) = (1 + 3y^2 ). Now, we can isolate .
2.
We take the derivative of each term with respect to x: − +
