Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#3

 

Question

Given that , x > 0 , find

a.   .

b.   .

c.  

Solution

a.
 

We are required to find .

Therefore, we are required to differentiate;

We are required to find .

Rule for differentiation of  is:

Rule for differentiation of  is:

b.
 

We are required to find .

Second derivative is the derivative of the derivative. If we have derivative of the curve   as  , then  expression for the second derivative of the curve  is;

We have found  in (a) as;

Therefore;

Rule for differentiation of  is:

Rule for differentiation of  is:

c.
 

We are required to find .

We are given;

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of  is:

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