Intro to derivatives
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This document introduces derivatives and their rules of calculation. It defines a derivative as the slope of the tangent line to a function's graph at a given point. It shows a graphic demonstrating a tangent line and provides the point-slope formula. It then lists some common derivative rules, such as the power, exponential, constant, and product rules, to calculate the derivatives of basic functions.
Intro to derivatives
- 1. Intro to Derivatives Tyler Murphy September 15, 2014 1 Introduction First, what is a derivative? To understand the derivative, we must
- 2. rst understand some- thing called a tangent line The tangent line is a line that intersects the graph at only one point. See Figure 1. Figure 1: A Tangent Line Point-Slope form of a line y y1 = m(x x1) infomal de
- 3. ntion The derivative of a function gives the slope of the tangent line. 2 Derivative Rules Name Function (f(x)) Derivative (f0(x)) Power Rule axn naxn1 Exponential ex ex Constant Function a 0 Scalar a f(x) a f0(x) Sum f(x) + g(x) f0(x) + g0(x) Product Rule f(x) g(x) g(x) f0(x) + f(x) g0(x) Quotient Rule f(x) g(x) f0(x) g(x) f(x) g0(x) f(x)2 1