Name:_____________________ Student Number: _______

1. Use the definition of the derivative only to compute the derivative of at x=1 (do not use rules of differentiation).

2. Compute the derivatives of the following functions (use the Power Rule, Product Rule, Quotient Rule, Chain Ruler, .). Do NOT simplify your answer.

(a)

(b)

(a)

(b)

3. Find an equation of the tangent line to the curve at the point .

Note first that when x=1, we have . So, the tangent line is through the point (1,1). An equation of such a line is , where is the slope of the line. But, as we know, the slope of the tangent line is . To find this we first compute : , where in the last step we have used the chain rule. Now we find that . So, the tangent line has an equation .