Author: Catherine

This is when “y” is not isolated. We are used to seeing y=2x +1 (explicit diff), however there are instances where y+1=2x (implicit diff). In implicit differentiation, our objective is to isolate the “y” by 1) Deriving both sides of the equations (note: we ALWAYS use chain rule to derive y). 2) Then isolating y’.…

This is where you are required to derive a function within a function (otherwise known as composite functions, recall pre calc 12). In chain rule there are cases where you will have to use power, product, quotient rules etc. for the inner function–or even chain again! You should have a good basis in all the…

The two main Trigonometric Derivatives that you will need to know are: d(sinx)/dx=cosx d(cos)/dx=-sinx However there are several others (tanx, cotx, secx, cscx) that are also useful to memorize. Derivatives of Trigonometric Functions (cr: Organic Chemistry Tutor) You will see functions that look like: sin2x and may wonder how to derive/solve these. We will be…

This is where you derive, take the derivative of the last derivative, then continue on. You will be utilizing all of power, sum/diff, product, quotient and chain (next lesson, 2.5) rules here. Higher Order Derivatives (cr: Organic Chem Tutor)

Utilizing the power rule, you will use these rules below for complicated derivatives Product Rule: y’= f’g+g’f Quotient Rule y’= f’g-g’f/g² “Mr. S explains when you should and shouldn’t use the quotient rule using examples of functions. I liked how he used examples instead of using words to explain, as it makes it easier to…

Power rule: If f(x)= 2x² then f'(x)= 2*2x²⁻¹->4x. Very fun rule! You will be using this as the basis to use product, quotient, chain rules and solve various other complicated derivatives. Sum and Difference Rule: Utilizing the power rule, if f(x)=2x² + 3x⁴ then, f'(x)= 4x +12x³, essentially power ruling each term. Derivatives – Power…

Essentially a derivative is the slope of a given any point on a function, other wise known as the instant rate of change on the point (△y/△x). The literal and formalized definition of the derivative is the following formula: “Visual Derivative Definition” (cr: Math Visual Proofs) To solve problems using this formula, you will need…

Here you will separated variables into their derivatives and then integrating them. These are indefinite integrals so you will need the variable “c” on the “x variable” side of the equation. Separable First Order Differential Equations – Basic Introduction (cr: Organic Chem Tutor) NOTE: Sometimes after integrating 1/y you will end up with a natural…

Good visualization website: https://www.geogebra.org/m/Fayr3trM Disc Method: Given a function, we rotate this around the x-axis (or y-axis), creating multiple discs/circles from the start to the end of the functions. Summing up the area of these circles (recall: πr²). Volume of the Solid of Revolution, the Disc Method (cr: Blackpen Redpen) Washer Method: This is similar…