Derivatives of Trig Functions. Example Problem
Find the slope of the line tangent to the graph of g of x equals 2x cubed, times sine x, 1x equals pi. So slope of the line tangent, that is a dead giveaway that we’re doing a derivative when x equals pi – find g prime of pi. We’re going to take the derivative of this function g,we are multiplying two variable expressions together, that’s a product rule. We’ll call that f, we’ll call that g. The derivative of f times g, is f*g prime plus fprime g. F times the derivative of g, derivative of sine x is cosine × 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 times sine pi. Sine of pi recall is 0, and cosine of pi is negative 1. So the answer would be negative 2 pi cubed. Find the slope of the line tangent to g(x)=2x^3 *sinx when x=pi -> g'(pi) g'(x)=2x^3*cosx+6x^2*sinx g'(pi)=2pi^3*cos(pi)+6(pi)^2*sin(pi) – sin(pi)=0 g'(pi)=-2pi^3 d/dx(f*g)=fg’+f’g
