### Day 68 - Bases Other Than e - 11.25.14

 UpdatesN/ABell Ringer QuizDifferentiation/Integration of Natural Log and Exponential FunctionsFind the derivative with respect to x of the following: .all of the abovenone of the aboveFind .both b and cnone of the abovenone of the aboveFind of the following: none of the aboveReviewAlgebraDifferentiation of the Natural Logarithmic FunctionIntegration with the Natural Logarithmic FunctionExponential Functions: Differentiation and IntegrationLessonBases Other Than eCheckpoints$\int\sin(x)dx=-\cos(x)+C$$\int\cos(x)dx=\sin(x)+C$$\int\tan(x)dx=-\ln |cos(x)|+C$$\int \csc(x)dx=-\ln|\csc(x)+\cot(x)|+C$$\int \sec(x)dx=\ln|\sec(x)+\tan(x)|+C$$\int \cot(x)dx=\ln|\sin(x)|+C$Exit TicketPosted on the board at end of the block. Lesson Objective(s)How are derivatives found when bases are not e?Standard(s)APC.9Apply formulas to find derivatives.Includes:derivatives of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functionsderivations of sums, products, quotients, inverses, and composites (chain rule) of elementary functionsderivatives of implicitly defined functionshigher order derivatives of algebraic, trigonometric, exponential, and logarithmic, functionsMathematical Practice(s)#1 - Make sense of problems and persevere in solving them#2 - Reason abstractly and quantitatively#5 - Use appropriate tools strategically#6 - Attend to precision#8 - Look for and express regularity in repeated reasoningPast CheckpointsDifferentiation of the Natural Logarithmic FunctionCheckpointsIntegration with the Natural Logarithmic FunctionCheckpointsExponential Functions: Differentiation and IntegrationCheckpoints