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This is a basic example of a very important result: the chain rule. The difficulty of this sort of example is that we have a "function of a function". That is, we have the function '4-x' and ...

For this question the chain rule should be used, the chain rule is that dy/du*du/dx=dy/dx.

If we say u=(x²+2x) and therefore y=e^u

Then du/dx=2x+2 and d...

We can differentiate this implicitly by writing the question as:y = 2^x Then we take the log of both sides:ln(y) = ln(2^x)Using the rules of logartithms this can be written as:ln(y) = ...

to differentiate this equation we have to do it in two parts because there is a minus sign seperating them in the middle

for the first part we first have to multiple the constant by what ...

First of all you need to separate the two numbers 

you have 8Y

and 4y2

then ask yourself what you can divide both these 2 numbers with? so 4 can be divided by ...