Grouping the terms, you get
sin y − x = y − 1Now factor out .
(sin y − x) = y − 1The derivative is
PROBLEM 3. Find the derivative of each variable with respect to t of x^2 + y^2 = z^2.
Answer: 2x + 2y = 2z
PROBLEM 4. Find the derivative of each variable with respect to t of V = πr^2 h.
Answer:
PROBLEM 5. Find if y^2 = x^2 − 2x
Answer: First, take the derivative with respect to x.
2 y = 2x − 2Then, solve for .
The second derivative with respect to x becomes