Derivatives of Trig Functions: Applications

1. Find the slope of the tangent to the curve y = x^{2} – sin^{2} x at x = 2.

The slope is, of course, the derivitive, so:

dy/dx = 2x – 2sin x cos x

dy/dx = 2(2) -2sin(2) cos(2) = 4.757

(Note that we use 2 radians.)