# 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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