4. Applications of Derivatives

Evaluate and simplify y'.

sin x cos(y−1) = 1/2

Differentiating Implicitly

Use implicit differentiation to find dy/dx in Exercises 1–14.

x = sec y

51–56. Second derivatives Find d²y/dx².

2x²+y² = 4

Find by implicit differentiation.

x² + xy + y² - 5x = 2

45–50. Tangent lines Carry out the following steps. <IMAGE>

b. Determine an equation of the line tangent to the curve at the given point.

(x²+y²)²=25/4 xy²; (1, 2)