Learn: Differentiation

Welcome!Today we'll explore differentiation, a key topic in AQA A Level Mathematics. This concept helps us understand how quantities change and is widely applied in real-world situations like physics and economics.

What is Differentiation?Differentiation is a mathematical process used to find the rate of change of a function. In simpler terms, it allows us to measure how one quantity changes in relation to another. For example, it helps calculate the speed of a moving object when its position changes over time.

The Gradient of a CurveOne key use of differentiation is finding the gradient (steepness) of a curve at any point. The gradient represents how steep the curve is and whether it is increasing or decreasing at that point.

Finding DerivativesThe result of differentiation is called the derivative. It is often written as dy/dx, where 'y' is the function and 'x' is the variable. This tells us the rate at which 'y' changes as 'x' changes.

Basic Rules of DifferentiationTo differentiate functions easily, we use rules such as:Power Rule: If y = xn, then dy/dx = nxn-1.Constant Rule: If y = c (a constant), then dy/dx = 0.Sum Rule: If y = u + v, then dy/dx = du/dx + dv/dx.

Applications of DifferentiationDifferentiation is used to find:Rates of change: For example, velocity is the rate of change of displacement.Gradients: To measure how steep a curve is at a specific point.Optimisation: To find maximum or minimum values in problems, like profit or cost.

Review Time!Great work! You've learned about differentiation, derivatives, gradient, and applications. Let's test your understanding with some questions.