MATH137 Study Guide - Final Guide: Slope Point, Product Rule, Riemann Sum

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: Frank Zorzitto

Document Summary

Find the derivative of ( ) ( ) Note that this function can be rewritten as a composition ( ) , where . The chain rule in this case is referred to as the power of a function rule. It is used when the exponent applies not just to a single x, but to an entire function. Note: if e or a are raised to some function (ie. not just x on its own), then we must apply chain. Find the equation of the tangent to ( ) at. Thus, the slope of the tangent at x = 1 is . At x = 1, we have ( ) . Therefore, in slope- point form, the equation of the tangent is: Note: if a trig function is applied to some function (ie. not just x on its own), then we must apply chain rule. Find the points where the tangent to ( )