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To begin to solve this equation we must take natural logarithms of both sides of the equation. This gives: ln(3^x*e^4x) = lne^7 Then we can use the log rules on the left hand side to expand it slightly to: l...

Suppose we have a matrix M = [{a b} {c d}] The inverse of a matrix M is any matrix, that when multiplied by M, gives the unit matrix (I) - in this case: [{1 0} {0 1}] First, we have to determine if the matri...

To make this equation easier to differentiate it would be easier to write it using index rules as y = 4x^3 - 5x^-2 From here we can begin to differentiate: dy/dx = 3*4x^(3-1) - (-2)*5x^(-2-1) Then finally si...

Firstly, let's split the equation "xcosx" into two parts to integrate them separately. 1) Let u=x and dv/dx=cosx 2)As the integral of x is 1, du/dx=1 3)To find v, we integrate cosx to get v=sinx Us...

In maths when we are asked to re express something we really only have 2 tricks. Multiply by 1, or add Zero. The hard part is finding how to express 1 or zero to suit the problem. For this one we should mult...