Special derivatives

The  exercise appears under the Differential calculus Math Mission. This exercise practices understanding and basic derivatives with a handful of common function from calculus.

Types of Problems
There are four types of problems in this exercise:


 * 1) Select the correct value of the derivative: This problem provides a function and asks the student to find the value of the derivative of the function at a particular point. The student then selects the answer from a multiple choice list.Speder1.png
 * 2) Write the correct value of the derivative: This problem provides a function and asks the student to find the value of the derivative of the function at a particular point. The student then writes the answer in the space provided.Speder3.png
 * 3) Find the horizontal tangents of the function rule: This problem provides a function rule and asks the student to find the x-value where the function has a horizontal tangent line.Speder2.png
 * 4)  Find the horizontal tangents from graph and rule: This problem provides a rule with a graph and asks the student to find the x-value(s) where the function has a horizontal tangent line.Speder4.png

Strategies
Knowledge of a few basic derivatives and the meaning of the derivative would help to ensure success on this exercise.
 * 1) There are no need for combining derivatives (for example, no product rules).
 * 2) The functions involved are sine, cosine, tangent, ln and e^x whose derivatives are cosine, negative sine, secant squared, 1/x and e^x respectively.
 * 3) A horizontal tangent occurs when the first derivative is equal to zero. This is because the first derivative represents the slope of a tangent line, and a line is tangent if the slope is zero.

Real-life Applications

 * 1) Derivatives are used to describe the rate at which a function is changing.
 * 2) Many examples in the beginning of calculus are operations on a handful of different functions, including those in this exercise.