Differentiate y = 2xln(x)
This is an example of a question where you would use the product rule, where if y = uv then dy/dx = udv/dx + vdu/dx. In this case u = 2x and v = ln(x). So first of all we will differentiate 2x which is fairly easy and is equal to 2 and then we will differentiate ln(x) which is slightly harder and equal to 1/x, this is one that you will have to learn by heart.
Now that we have the differentials of 2x and ln(x) we can put it all together to find the differential of y. So by using the product rule from earlier dy/dx = 2x*(1/x) + ln(x)*2 which when we simplify is equal to 2( 1+ln(x) ).
TW
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