Unit 3: Calculus – Differentiation

February 17, 2026

Semester 1
BP106RMT

Introduction to Calculus – Differentiation

Unit 3 introduces ‘Calculus’, the mathematics of change. ‘Differentiation’ allows us to calculate rates—how fast a drug dissolves, how quickly blood concentration rises, or the slope of a curve. You will master the standard formulae and rules (Product, Quotient) needed to solve these problems.
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Syllabus & Topics

  • 1Differentiation: Introduction, Derivative of a function
  • 2Rules: Derivative of constant, Sum/Difference of two functions
  • 3Product Formula (uv rule) & Quotient Formula (u/v rule)
  • 4Standard Derivatives: x^n, e^x, log_e x, a^x
  • 5Trigonometric functions (sin x, cos x, tan x)
  • 6Successive Differentiation (First and Second order derivatives)
  • 7Application: Conditions for a function to be a maximum or a minimum

Learning Objectives

State the standard derivatives of algebraic and trigonometric functions.
Apply the Product and Quotient rules to differentiate complex functions.
Find the first and second derivatives of a given function.
Identify the critical points (maxima/minima) of a curve.
Relate differentiation to ‘Rate of Change’ in physical problems.

Frequently Asked Questions (FAQs)

Q1. What is Differentiation?

Differentiation is the mathematical process of finding the derivative, which represents the rate of change of a function. In pharmacy, it is useful for determining the rate of drug dissolution or drug elimination.

Q2. Standard derivative of a constant?

The derivative of any constant (such as 5, π, or e) is always zero, because a constant value does not change with respect to the variable.

Q3. What is the Product Rule?

The Product Rule for differentiation states:

ddx(uv)=u dv/dx+v du/dx

It is used when differentiating the product of two functions.

Q4. What is Successive Differentiation?

Successive differentiation is the process of differentiating a function repeatedly, such as finding the second derivative d2y/dx2. It is often used to determine quantities like acceleration from velocity.

Q5. Condition for Maxima and Minima?

For a function y = f(x) to have a maximum or minimum at a point:

  • The first derivative dy/dx=0

  • The second derivative determines the nature:

    • d2y/dx2<0 → Maximum

    • d2y/dx2>0 → Minimum