First Principles Differentiation What is the derivative or gradient function? For a curve?y?=?f(x)?there is an associated function called the?derivative?or?gradient function The derivative of f(x) ...
Definition of Gradient What is the gradient of a curve? At a given point the?gradient?of a curve is defined as the gradient of the?tangent?to the curve at that point A?tangent?to a curve is a line ...
Using Log Graphs in Modelling What are log graphs? Log graphs are used when the scale of a graph increases or decreases exponentially It can very difficult to read specific values from graphs with ...
Using Exps & Logs in Modelling What is exponential modelling? Exponential modelling is where real-life situations are modelled using exponential growth and decay Exponential growth is typically...
Exponential Growth & Decay What are exponential growth and exponential decay? y = Aekt?is exponential?growth y = Ae-kt?is exponential?decay k > 0?so plus or minus sign in equation immediatel...
Exponential Equations What are exponential equations? An equation where the unknown is a power In simple cases the solutions can be “spotted” How do I solve exponential equations? Laws of In...
Laws of Logarithms What are the laws of logarithms? There are many laws or rules of indices, for example There are equivalent laws of logarithms (for a > 0) There are also some particular result...
Derivatives of Exponential Functions What is the derivative of e? y = ex?has the particular property ie for?every?real number?x, the gradient of?y = ex?is also equal to?ex?(see Derivatives of Expon...
"e" Exponential Function What is e, the exponential function? The exponential function is?y = ex e?is an?irrational?number e ≈ 2.718 As with other exponential graphs?y = ex passes through (0, 1) ha...
