Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

How To Find Derivatives Using Implicit Differentiation: Example With F(X)G(Y) = 17 – X – Y

The point (−2,4) lies on the curve in the xy-plane given by the equation f(x)g(y)=17−x−y, where f is a differentiable function of x and g is a...

John Rhodes
June 21, 2023
Calculus

Finding F(0) And G'(2) Using Inverse Function Theorem In Math – Step By Step Guide

Let f be the increasing function defined by f(x)=x3+2×2+4x+5, where f(−1)=2. If g is the inverse function of f, which of the following is a correct expression...

John Rhodes
June 21, 2023
Calculus

How To Find The Derivative Of An Inverse Function: Step-By-Step Guide With Examples.

The table above gives selected values for a differentiable and decreasing function f and its derivative. If g(x)=f−1(x) for all x, which of the following is a...

John Rhodes
June 21, 2023
Calculus

How To Differentiate Sin⁻¹(X) Using The Chain Rule | Math Tutorial And Example Problem

ddx(sin−1x)∣∣x=12= Correct. If y=sin−1xy=sin⁡−1x, then siny=xsin⁡y=x. Using the chain rule to differentiate this implicit relation gives cosydydx=1⇒dydx=1cosycos⁡ydydx=1⇒dydx=1cos⁡y. Since y=sin−1xy=sin⁡−1x implies that −π2≤y≤π2−π2≤y≤π2, the value of cosycos⁡y is...

John Rhodes
June 21, 2023
Calculus

Mastering Integration By Parts In Calculus: A Comprehensive Guide

Integration by parts formula ∫udv= uv-∫vdu The integration by parts formula is a technique used in calculus to integrate the product of two functions. It is often...

John Rhodes
June 21, 2023
Calculus

Proving 1 + Tan^2X = Sec^2X Using Trigonometric Identity

1 + tan^2x = sec^2x sec^2x To prove that 1 + tan^2x = sec^2x, we will use the trigonometric identity: sec^2x = 1 + tan^2x Now, let’s...

John Rhodes
June 21, 2023
Calculus

Mastering Trigonometric Identities: Simplifying Expressions Using 1 + Tan^2X = Sec^2X Identity

1 + cot^2x = csc^2x We can start by using the identity: 1 + tan^2x = sec^2x. If we divide both sides by tan^2x, we get: 1/tan^2x...

John Rhodes
June 21, 2023
Calculus

Discover The Pythagorean Identity: Sin^2X + Cos^2X = 1

sin^2x + cos^2x = 1 The expression sin^2x + cos^2x equals 1. This is a fundamental trigonometric identity known as the Pythagorean identity. It states that the...