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QuestionThe average temperature in May is 18 ºC.The average temperature in November is a third of the average temperature in May.The average temperature in September is twice the average temperature in Novem...

The quick answer is that d/dx a^x = ln(a) * a^x. But why? Well, let's go through the steps so we can understand why the formula works. Firstly, a^x can be written as (e^(ln(a)))^x because e^(ln(z)) = z as th...

We are tasked with differentiating y = sin(x 2 ) ln(5x) This function is actually a product of the functions: sin(x 2 ) and ln(5x) Therefore the product rule will be required. First let's calculate the deriv...

Solving cubics is an interesting problem: while there is a formula which can find the roots of every cubic equation, it isn't taught and is not generally worth learning. Instead, exam questions will often gi...

We recall that a function f(x) is said to be an odd function when f(-x)=-f(x) . We are told that f(x) and g(x) are odd functions, so we know from the above definition that: 1. f(-x)=-f(x) 2. g(-x)=-g(x) Solu...