Math Problem Statement

just give me the answer, no need for explainaiton

Let u(x) = f(x)g(x) and v(x) = f(x)/g(x). Find u'(1) and v'(5).

Solution

The answer for part (b), v′(5)v'(5), is −1-1.

Would you like further details or have any other questions? Here are 5 related questions for practice:

  1. What is f′(5)f'(5)?
  2. What is g′(5)g'(5)?
  3. What is the value of v(5)v(5)?
  4. How would you find v′(x)v'(x) in general using the quotient rule?
  5. What is the geometric interpretation of f′(x)f'(x) and g′(x)g'(x)?

Tip: When applying the quotient rule, ensure to properly differentiate both the numerator and denominator before simplifying.

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Math Problem Analysis

Mathematical Concepts

Product Rule
Quotient Rule
Differentiation

Formulas

Product Rule: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x)
Quotient Rule: (f(x)/g(x))' = (f'(x)g(x) - f(x)g'(x)) / g(x)^2

Theorems

Differentiation Rules

Suitable Grade Level

Grades 10-12

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