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# MATH 1225 - Test 2 Study Guide MATH 1225

Virginia Tech

GPA 4.0

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## About this Document

## 249

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## Popular in Calculus of a Single Variable

## Popular in Mathematics (M)

This 3 page Study Guide was uploaded by Gavin B on Tuesday March 1, 2016. The Study Guide belongs to MATH 1225 at Virginia Polytechnic Institute and State University taught by Eun Chang in Fall 2015. Since its upload, it has received 249 views. For similar materials see Calculus of a Single Variable in Mathematics (M) at Virginia Polytechnic Institute and State University.

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Date Created: 03/01/16

VT - MATH 1225 - UNIT 2 TEST 2 STUD Y GUIDE Not Differentiable When: there is jump discontinuity, sharp turns (vertical tangent), includes absolute value and cubic root of x. If it is differentiable then it is continuous but just because it is continuous Distribution rules. differentiable. Derivatives: d dxsin x=cosx d cos x=−sin x dx d tan x=sec x dx d csc x=−cot xcscx dx d secx=tan xsec x dx d cot x=−csc x dx Product Rule, Quotient Rule, Chain Rule. d b =b ∗ln∗du dx dx VT - MATH 1225 - UNIT 2 Implicit Differentiation: Take derivative of both sides, solve for dy if dx that is what is what you are being asked for. If asked to find equation of tangent line, find derivative that is slope and then use point slope formula. Derivatives of Inverse Trigonometric Functions: To find derivatives of inverse trig functions switch y and x and get rid of the -1 above the trigonometric function. Once you get a trigonometric value use the trigonometric formulas so you can substitute the original trigonometric function back in and then some sort of x for that. d sin x= 1 dx 2 √ 1−x d −1 −1 dxcos x= 2 √1−x d −1 1 dxtan x= 2 1+x d −1 −1 dxcsc x= 2 |x|√x −1 d −1 1 sec x= 2 dx |x|√x −1 d −1 −1 cot x= 2 dx 1+x Trigonometric Identities: 2 2 sin x+cos x=1 tan x+1=sec x2 2 2 1+cot x=csc x Log Rules: logabc=log a+log ca log b=log b−log c a c a a c c logab =clog a , lnb =clnb lnb logab= lna Know how to get derivative of a log. To do log differentiation, take the log (ln in all cases from class) of both sides. Δ y f( 2− f (x1) Average rate of change: Δ x= x −x 2 1 For when is particle moving forward question use a number line and put in 0 solutions. Object is speeding up when velocity and acceleration have same signs and object is slowing down when velocity and acceleration have different signs. VT - MATH 1225 - UNIT 2 Related Rates: Write down equation. Differentiate both sides. Plug in values. Solve for the derivative of what you want. Linearization: L(x)= f (a+ f (a)(x−a) Differentials: ' because dy = f (x) dy= f (x)∗dx dx Newton’s Method: x =x − f (xn) n+1 n f (x ) n Derived from Linearization equation. sin x lim x =1 x→ ∞

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