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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 ...

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...

Firstly, we are given that f(x) can be expressed in the above form, so we write this out:

(19x-2)/((5-x)(1+6x)=A/(5-x)+B/(1+6x)

We then multiply by the denominator of f(x):<...