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A key point to remember here is that a^x could mean the base (a) is not “e”-that special number which has a gradient function, dy/dx (the differential), EQUAL to the function itself, y=e^x. When "a&q...

By recalling that e^ln(a) = a, you can rewrite 3^2x as e^2xln(3).

Then, you can differentiate this like any other e function, by using the product rule.

First, find the x coordinates of where the lines intersect by setting the equations of the lines equal to each other. Then solve the quadratic (or polynomial) equation. Next, integrate both lines indiv...

The expectation of x, E(X), is the sum of the product of the value of the i^th outcome (x_i) and the probability of the i^th outcome (p_i). So:

E(X...

To tackle this question, you will need to know about the rules for logarithms. Here we are going to use the product rule, where the addition of these two natural logarithms equals the product of the tw...