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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 ...

If you imagine that sin(x), cos(x), -sin(x) and -cos(x) are on a wheel as shown below:

      sin(x)

-cos(x)  cos(x)

     -sin(x)

then going clock...