Mathematics | Senioritis

John Rhodes
June 21, 2023
Calculus

Find the Equation of the Line Tangent to the Graph of f at x=-1 – A Step-by-Step Guide.

The derivative of the function f is given by f′(x)=−3x+4 for all x, and f(−1)=6. Which of the following is an equation of the line tangent to...

John Rhodes
June 21, 2023
Calculus

Why f(2) Exists Only When f is Continuously Defined at x=2: the Relationship Between Continuity and Function Existence

Which of the following statements, if true, can be used to conclude that f(2) exists?i. limx→2f(x) exists.ii. f is continuous at x=2.iii. f is differentiable at x=2....

John Rhodes
June 21, 2023
Calculus

Proving the Derivative of sin(x) = cos(x) with the Fundamental Formula

Derivative of sin x cos x The derivative of sin x is cos x. To prove this, we can use the fundamental derivative formula that states that...

John Rhodes
June 21, 2023
Calculus

Mastering the Quotient Rule of Differentiation: Derivative of Tan x Simplified to Sec^2 x

Derivative of tan x sec^2 x The derivative of tan x can be found using the quotient rule of differentiation. Recall that tan x = sin x...

John Rhodes
June 21, 2023
Calculus

Master the Quotient Rule and Trigonometric Identities to Find the Derivative of Sec x

Derivative of sec x sec x tan x The derivative of sec x can be found using the quotient rule and trigonometric identities. Recall that sec x...

John Rhodes
June 21, 2023
Calculus

How to Find the Derivative of Cot x Using the Quotient Rule in Calculus

Derivative of cot x -csc^2 x The derivative of cot x can be found using the quotient rule: Let f(x) = cos x and g(x) = sin...

John Rhodes
June 21, 2023
Calculus

Learn How to Find Derivative of ln x with Logarithmic Differentiation – Calculus Tutorial

Derivative of ln x 1/x The derivative of ln x is simply 1/x. To find the derivative of ln x using calculus, we can use the logarithmic...

John Rhodes
June 21, 2023
Calculus

How to Find the Derivative of b^x Using Logarithmic Differentiation and Chain Rule

Derivative of b^x b^x ln(b) The derivative of b^x with respect to x can be found using logarithmic differentiation or the chain rule. Using logarithmic differentiation: y...