Differential And Integral Calculus By Feliciano And Uy Chapter 4 !link! May 2026

Chapter 4 of the classic textbook Differential and Integral Calculus by Feliciano and Uy is titled "Differentiation of Transcendental Functions".

  1. Identify a governing equation (e.g., Pythagorean theorem).
  2. Implicitly differentiate with respect to time ( t ).
  3. Substitute known values (be careful: the rate of the top is negative while the bottom is positive).

Feliciano and Uy then discuss the applications of maxima and minima in various fields, including: Chapter 4 of the classic textbook Differential and

III. Step-by-Step Workflow for Solving Problems

Step 1: Identify the outer trigonometric function (sin, cos, tan, etc.). Step 2: Identify ( u ) (the inside function). Step 3: Differentiate the outer function (keeping ( u ) intact). Step 4: Multiply by ( \fracdudx ) (derivative of the inside). Step 5: Simplify using algebraic identities (e.g., ( \sin^2 x + \cos^2 x = 1 )). Identify a governing equation (e

  • Critical points – solve (f'(x)=0).
  • Increasing/Decreasing – sign of (f'(x)).
  • Local extrema – use 1st or 2nd derivative test.
  • Concavity & inflection points – sign of (f''(x)).
  • Plot points & sketch curve.

    • 1. Tangents and Normals

    The chapter opens with a review of geometric interpretation. You will learn how to find the slope of a curve at any given point, but more importantly, you will solve for: Feliciano and Uy then discuss the applications of

    Show Every Step: Don't skip steps when applying the Quotient Rule. One missed sign in the numerator will ruin the entire result.

    • Differentiate: 2x + 2y (dy/dx) = 0 → dy/dx = −x/y.