Example Problem. Derivatives of Trig Functions

p {margin: 0; padding: 0;} .ft00{font-size:19px;font-family:CourierNew;color:#000000;} .ft01{font-size:16px;font-family:CourierNew;color:#000000;} .ft02{font-size:16px;line-height:18px;font-family:CourierNew;color:#000000;} Derivatives of Trig Functions. Example Problem Find the slope of the line tangent to the graph of g of x equals2x cubed, times sine x, 1x equals pi. So slope of the line tangent, that is a dead giveaway that we'redoing a derivative when x equals pi - find g prime of pi. We're going to take the derivative of this function g,we aremultiplying two variable expressions together, that's a productrule. We'll call that f, we'll call that g. The derivative of f times g, is f*g prime plus f prime g. F times the derivative of g, derivative of sine x is cosinex plus the root of 2x cubed, that's 6x squared times sine x. And then we're going to evaluate when x is pi.So it's 2 pi cubed times the cosine of pi plus 6 pi squared timessine pi.Sine of pi recall is 0, and cosine of pi is negative 1. So the answer would be negative 2 pi cubed.