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y=5x

The change in Y over the change in X gives the differential of 5x

As the power of 'x' is 1, this is brought down and multiplied by 5 and the power of x is 1-1 = 0. Therefore, the power ...

x^x=e^x*ln(x)

So  d/dx (x^x) = d/dx (e^x*ln(x))

By chain rule, we get     d/dx (xln(x))e^xln(x) 

Then by product rule we get...

Draw the sine graph on a whiteboard. Infer graphically by drawing the line y = a. As 0

x + 3x^-1 + 2(x-2)^-1 - 1(x-2)^-2

An infinite geometric series is of the form a*(1 + b + b^2 + b^3 ...)

To find the sum of all the terms in this series we consider the sum, S, where:

S= 1 + b + b^2 + b^3 ... + b^n

whe...