Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Proving The Derivative Formula: Sin(X) To Cos(X) Using The Definition Of The Derivative

derivative of sinx cosx The derivative of sin(x) is cos(x). To prove this, we can use the definition of the derivative: f'(x) = lim(h -> 0) [f(x+h)...

John Rhodes
June 21, 2023
Calculus

Learn How To Find The Derivative Of Tan(X) Using The Quotient Rule

derivative of tanx sec^2x The derivative of tan(x) can be found using the quotient rule: Let y = tan(x) Then y’ = (sec^2(x))(1) – (tan(x))(sec^2(x))(1) Simplifying this...

John Rhodes
June 21, 2023
Calculus

Step-By-Step Guide: How To Find The Derivative Of Sec(X) Using The Quotient Rule

derivative of secx secxtanx The derivative of sec(x) can be found using the quotient rule of differentiation, because sec(x) can be expressed as 1/cos(x): sec(x) = 1/cos(x)...

John Rhodes
June 21, 2023
Calculus

Mastering The Derivative Of Cot X: Using The Quotient Rule For Trigonometric Identities

derivative of cotx -csc^2x The derivative of cot x can be found using the quotient rule. Let us denote certain trigonometric identities: cosec^2 x = 1/sin^2 x,...

John Rhodes
June 21, 2023
Calculus

Discover How To Find The Derivative Of Arcsin X Using Implicit Differentiation

derivative of sin^-1 1/√(1-x^2) The derivative of sin^-1(x) (also expressed as arcsin x or inverse sine of x) can be found using implicit differentiation. Let y =...

John Rhodes
June 21, 2023
Calculus

Discovering The Derivative Of Arctan (Tan^-1): A Step-By-Step Guide

derivative of tan^-1 1/(1 + x^2) The derivative of arctan (tan^-1) is: d/dx arctan(x) = 1 / (1 + x^2) This can be derived using the formula...

John Rhodes
June 21, 2023
Calculus

Continuity In Mathematics: A Guide To Smooth, Uninterrupted Functions

Definition of Continuity:1) ___________________2) ___________________3) ___________________ 1) f(c) is defined2) lim x->c of f(c) exits3) lim x-> c of f(x) = f(c) 1) Continuity is a property...

John Rhodes
June 21, 2023
Calculus

Proving Root Existence: The Importance Of The Intermediate Value Theorem In Calculus And Real Analysis

Intermediate Value Theorem:1) ___________________2) ___________________3) ___________________ then there exits a number c between a and b for which f(c) = k 1) f(x) is continues on [a,b]2)...