Calculus I (Differential Calculus)
Calculus I is designed primarily for those students planning to pursue programs in engineering, mathematics, computer science, and physical sciences. This course includes topics of differential and integral calculus of a single variable. This course contains a series of video tutorials that are broken up in various levels. Each video builds upon the previous one.
In this first course in Calculus (Differential Calculus) you will learn various differentiation rules that will allow you to find derivatives without the direct use of the limit definition. We will first learn how to find the derivative of polynomials and natural exponential functions.
Then we will shift gears and learn how to apply the product and quotient rule. We will then learn how to find the derivative of trigonometric functions. After that, we will learn how to use the chain rule to find the derivative of more complicated functions.
We will then learn how to differentiate via implicit differentiation. We will follow up with derivatives of inverse Trigonometric Functions and logarithmic functions. We will end the video series by learning how to differentiate via logarithmic differentiation.
After going over these videos you should be armed with the basic skills necessary to find the derivative of various functions.
Introduction
Derivatives of Polynomials and Natural Exponential Functions
This video introduces basic differentiation rules to find the derivative of polynomials and natural exponential functions. This video covers the derivative of a constant, the power rule, and the derivative of a natural exponential function.
This video will teach how to rewrite common functional expressions into a "derivative friendly" form. A good understanding of intermediate algebra is required to succeed in any calculus class.
The Product Rule
This video will teach you how to find the derivative of functions formed by products of functions by using the product rule. An example involving the product of three functions is also illustrated.
This video continues going over how to find the derivative of functions formed by products of functions by using the product rule. This videos goes over 5 examples illustrating how to find the derivative of functions by writing a general expression and using values that are provided to find the derivative at a given value of x.
This video continues going over how to find the derivative of functions formed by products of functions by using the product rule. This videos goes over 2 examples illustrating how to find the derivative of functions by using the graphs of these functions.
The Quotient Rule
This video will teach you how to find the derivative of functions formed by a quotient of functions by using the quotient rule and going over 3 examples.
This video continuous going over more challenging example that require the use of the quotient. This video goes over 7 examples. 3 of these examples involves finding an expression for the derivative in terms of general functions.
This is the third and final video on the quotient rule. This video goes over 4 examples illustrating how to find the derivative of a function by using a set of values and by using the graphs of functions.
Derivatives of Trigonometric Functions
The Chain Rule
This video will teach you the basics of the chain rule. It includes a small review of composition of functions and various examples demonstrating how to break apart a function into its composite functions.
Implicit Differentiation
This video will teach you how to find the derivative of functions defined implicitly related by the dependent and independent variable.
Derivatives of Inverse Trigonometric Functions
Derivatives of Logarithmic Functions
Logarithmic Differentiation
This video will teach you how to use logarithmic differentiation to find the derivative of complicated functions formed by products, quotients, and powers. The video goes trough 3 different examples.
This video will teach you how to use logarithmic differentiation to find the derivative of functions where the base and exponent are them self's formed by functions. The video goes over various examples step by step.
