Differential Equations
Summary Differential Equation – any equation which involves or any higher derivative. Solving differential equations means finding a relation between y and x alone through integration. We use the method of separating variables in order to solve linear differential equations. We must be able to form a differential equation from the given information. What is … Read more
Implicit Differentiation
Summary An implicit equation is an equation which is not in the form , it consists of two variable x and y which cannot be separated. Implicit Functions are differentiated by using ”chain rule” in combination with the ”product and quotient rule”. When we differentiate y we write with the derivative i.e To find the … Read more
Parametric Differentiation
Summary When x and y are expressed in terms of a third variable it is called a parameter. To differentiate parametric equations to find derivative of y with respect to x, we use the chain rule method. When the parameter in the equations is “t”, the chain rule is defined as: What is parameter? We … Read more
The Second Derivative
Summary Second derivative is when we differentiate . We write second derivative of y with respect to x as: Stationary Points are obtained by solving the equation . Maximum point: Minimum point: Second derivative Differentiation is the process that we use to find the gradient of a point on the curve. We define a gradient … Read more
Exponentials & Logarithms
Summary is known as an exponential function Logarithmic functions are written as Laws of logarithm: 1. 2. 3. 4. 5. 6. Exponential functions When n is a positive integer and a is the base in , then n is known as the index, power or exponent. Suppose we have , this is called an exponential … Read more