Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#2
Question
,
a. Find , giving each term in its simplest form.
b. Find , giving each term in its simplest form.
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.
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;
From (a) we have;
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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