Power rule (advanced)

The  exercise appears under the Differential calculus Math Mission. This exercise uses the power rule from differential calculus.

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


 * 1) Find the rule for the derivative: This problem provides a polynomial function. The student is expected to type the entire derivative function in the space provided.PowrulB2.png
 * 2) Find the slope at the point: This problem has a polynomial function. The student is expected to find the value of the slope of the function at the specific point.PowrulB3.png
 * 3) Select the derivative function: This problem has a function and a multiple choice list with several other functions. The student is expected to take the derivative of the function, possibly with some simplification, and then select the derivative from the list.PowrulB1.png

Strategies
Knowledge and comfort with the power rule in differential calculus is encouraged to ensure success on this exercise.
 * 1) The derivative of ax^n is anx^(n-1).
 * 2) The distributive properties can be employed initially to make a function into a polynomial, from which the power rule can be used to directly.
 * 3) A radical is a fractional exponent.

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) Polynomials can be used via Taylor Series to represent many other functions.