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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