Symbolic differentiation

The  exercise appears under the Differential calculus Math Mission. This exercise practices derivative notation, specifically the "prime" notation.

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


 * 1) Find the derivative of the function: This problem provides a non-standard function and a value. The student is expected to find the value of the derivative at the given value.Symdif1.png
 * 2) Find the value of the differential expression: This problem has a differential expression and a table containing the value of the functions and their derivatives at particular points. The student is expected to find the final value of the expression and write it in the space provided.Symdif2.png
 * 3) Select equal or unequal expressions: This problem provides a beginning differential expression and various other expressions following it. The student is asked to select which, if any, of the expressions are either equal or unequal to the given expression.Symdif3.png

Strategies
Knowledge of the differentiation rules, as well as some basic derivatives are encouraged to ensure success on this exercise.
 * 1) The derivative operation is linear, so it pulls through addition, subtraction and constants pull out.
 * 2) The derivative of a piecewise function is the derivative of the portion where the function is being evaluated.
 * 3) These problems are called symbolic because derivative notation is used, not just slope.

Real-life Applications

 * 1) Calculus has massive applications to physics, chemistry, biology, economics and many other fields.
 * 2) The slope of a curve is the natural extension of a linear slope.
 * 3) The notation in this exercise is used to write the rules of calculus.