### Improve Competence with MyMathsHero

The instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point. It is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

In this topic, we cover the following: Gradient of a curve, gradient function, differentiation coefficient, dy/dx, rules of differentiation, application of differential calculus, reverse of differentiation. At the end of this topic, students should understand the following among other things:

- Find the gradient function of a simple quadratic curve and hence find the gradient of the curve at a given point,
- Apply different calculus to determine: rates of change including gradients, velocity and acceleration; turning points on a curve and curve sketching,

- Apply the idea of limits to determine dy/dx, the different coefficient of y with respect to x,
- Differentiate polynomials and use the chain rule, and the product quotient rules to differentiate complex algebraic expressions,
- Determine the equation of a line, or curve, given its gradient function,
- Use inverse of differentiation to find the general solutions of simple differential equations,