Chapter 2: Differentiation
What you need to learn in this chapter
- Apply the rules of differentiation to find the derivative of various functions
- Determine the second derivative of a function f(x) using the rules of differentiation
- Solve problems involving rates of change, tangents and normals, and optimization using differentiation
- Apply differentiation to solve problems involving related rates, maxima and minima, and curve sketching
In this chapter, we will learn about limits and how they relate to differentiation.
We will also explore first and second order differentiation, which involves finding the derivative of a function.
We will apply differentiation to solve various problems, such as finding the value of a limit, determining the first and second derivatives of a function, and solving problems involving rates of change, tangents and normals, and optimization.
Additionally, we will learn how to apply differentiation to solve problems involving related rates, maxima and minima, and curve sketching.
Topics in this chapter
1. Limit and its relation with differentiation
What you will learn in this topic
- Investigate and determine the value of a limit of a function when the variable approaches zero
- Determine first derivative of a function f(x) using first principle of differentiation
2. First Order Differentiation
What you will learn in this topic
- Deduce first derivative formula by induction for function n y ax^n , a is a constant and n is an integer
- Determine the first derivative of an algebraic function
- Determine the first derivative of a composite function
- Determine the first derivative of a function that involving the product and the quotient of an algebraic expression
3. Second Order Differentiation
What you will learn in this topic
- Determine the second derivative of an algebraic function
4. Application of Differentiation
What you will learn in this topic
- Interpret the gradient of a tangent to a curve at different points
- Determine the equation of a tangent and normal to a curve at one point
- Solving problems involving tangent and normal
- Determine the turning point and describe the properties of the turning point
- Solving problems involving maximum value and minimum value and interpret the solution
- Interpret and determine the rate of change for related quantities
- Solving problems involving the rate of change for related quantities and interpret the solution
- Interpret and determine the small change and approximation of a quantity
- Solving problems involving small change and approximation of a quantity
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