# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#4

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**Question**

**a. **Find , giving each term in its simplest form.

**b. **Find .

**Solution**

**a.
**

We are given;

We are required to find .

Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is:

Therefore;

Rule for differentiation is of is:

Rule for differentiation is of is:

Rule for differentiation is of is:

**b.
**

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;

Therefore, for the given case;

Rule for differentiation is of is:

Rule for differentiation is of is:

Rule for differentiation is of is:

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