In Exercise, expand the logarithmic expression. ln x(x + 1)

1 answer:

34kurt3 years ago

3 0

Answer:

dy/dx = 2x+1/x(x+1)

Step-by-step explanation:

y = In x(x+1)

Let u = x(x+1) = x^2 + x

du/dx = 2x + 1

y = In u

dy/du = 1/u

dy/dx = dy/du × du/dx = 1/u × 2x+1 = 2x+1/u = 2x+1/x(x+1)

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Answer:

$\displaystyle d = 2\sqrt{13}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Point (11, 4) → x₁ = 11, y₁ = 4

Point (5, 8) → x₂ = 5, y₂ = 8

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(5-11)^2+(8-4)^2}$
[√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{(-6)^2+(4)^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{36+16}$
[√Radical] Add: $\displaystyle d = \sqrt{52}$
[√Radical] Simplify: $\displaystyle d = 2\sqrt{13}$