logarithmic-differentiation-calculus-ab-bc-implicit-derivative

For more cool math videos visit my site at mathgotserved.com or http://youtube.com/mathsgotserved

In this clip we go over how to find the derivative of a complex function. The logarithmic differentiation method is employed here. The natural log logarithm of both sides are taken first then the funciton is differentiated implicitly and then solved for y prime dy/dx

The student will investigate derivatives presented in graphic, numerical, and analytic

contexts and the relationship between continuity and differentiability. The derivative will

be defined as the limit of the difference quotient and interpreted as an instantaneous rate

of change.

Mathematics Standards of Learning

60

APC.6 The student will investigate the derivative at a point on a curve. This will include

a) finding the slope of a curve at a point, including points at which the tangent is vertical

and points at which there are no tangents;

b) using local linear approximation to find the slope of a tangent line to a curve at the

point;

c) defining instantaneous rate of change as the limit of average rate of change; and

d) approximating rate of change from graphs and tables of values.

APC.7 The student will analyze the derivative of a function as a function in itself. This will

include

a) comparing corresponding characteristics of the graphs of f, f ', and f ";

b) defining the relationship between the increasing and decreasing behavior of f and the

sign of f ';

c) translating verbal descriptions into equations involving derivatives and vice versa;

d) analyzing the geometric consequences of the Mean Value Theorem;

e) defining the relationship between the concavity of f and the sign of f "; and

f) identifying points of inflection as places where concavity changes and finding points

of inflection.

APC.8 The student will apply the derivative to solve problems. This will include

a) analysis of curves and the ideas of concavity and monotonicity;

b) optimization involving global and local extrema;

c) modeling of rates of change and related rates;

d) use of implicit differentiation to find the derivative of an inverse function;

e) interpretation of the derivative as a rate of change in applied contexts, including

velocity, speed, and acceleration; and

f) differentiation of nonlogarithmic functions, using the technique of logarithmic

differentiation. *

* AP Calculus BC will also apply the derivative to solve problems. This will include

a) analysis of planar curves given in parametric form, polar form, and vector form,

including velocity and acceleration vectors;

b) numerical solution of differential equations, using Euler's method;

c) l'Hopital's Rule to test the convergence of improper integrals and series; and

d) geometric interpretation of differential equations via slope fields and the relationship

between slope fields and the solution curves for the differential equations.

APC.9 The student will apply formulas to find derivatives. This will include

a) derivatives of algebraic, trigonometric, exponential, logarithmic, and inverse

trigonometric functions;

b) derivations of sums, products, quotients, inverses, and composites (chain rule) of

elementary functions;

c) derivatives of implicitly defined functions; and

d) higher order derivatives of algebraic, trigonometric, exponential, and logarithmic,

functions. *

* AP Calculus BC will also include finding derivatives of parametric, polar, and vector

functions.

Mathematics Standards of Learning

61

Tagged under: product,quotient,exponential,quadratic,rule,power,logs,natural,properties,subsitution,implicit,differentiation,fractions,messy,classroom,101,instructional,video,lecture,bright,jmt,storm,khan,kellog,polynomials,algebra,guide,tutor,tutorial,tips,trick,-,test,scores,mathtv,mathchannel,prep,college,shortcut,key,ideas,math,mathematicas,cool,doctor,clinic,maths,mathematics,secrets,Guide,Answers,Tricks,Questions,Study,cheat,Algebra,placement,napier,inverse

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Dr Ayla Göl
@iladylayla

A good tool for supporting active #learning.

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!