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: