MATH 1680 Lecture Notes - Lecture 1: Asymptote, Quotient Rule, Tangent
Document Summary
A way to find the derivative of a complicated equation where a smaller function is in a larger function. Example: (cid:3052)(cid:3051) = (derivative of outside function leaving inside alone: (derivative of inside function) (cid:3052)(cid:3051) (cid:1877)=(cid:4666)(cid:885)(cid:1876)+(cid:883)(cid:4667)(cid:2875) How to find the equation of a tangent line with derivatives. 3 step 2: find derivative of just the inside. Step 3: multiply the derivative of the inside. slope. Find the equation of the tangent line to (cid:1877)=(cid:1876)(cid:2871)+(cid:884)(cid:1876)+(cid:884)(cid:1876) at the point (cid:4666)(cid:883),(cid:885)(cid:4667) Step 1: take the derivative of the equation given. Step 3: point slope formula (cid:1877) (cid:1877)(cid:2869) =(cid:4666)(cid:1876) (cid:1876)(cid:2869) ) Step 2: take the x-coordinate that you are given and plug it into x. The answer will be your (cid:1877) (cid:885)=(cid:887)(cid:4666)(cid:1876) (cid:883)(cid:4667) (cid:1877) (cid:2871)+(cid:2871)=(cid:887)(cid:1876) (cid:2873)+(cid:2871) Find the equation of the tangent line to the graph of (cid:4666)(cid:4667)= (cid:2778) at =(cid:2779). For (cid:4666)(cid:1876)(cid:4667)= (cid:3051)(cid:3051) (cid:2869) will need to use quotient rule.
