1. Compute the following derivatives, showing all work as required.

(a.) Using first principles, differentiate ()=()^2/3 (Hint: use the 'difference of cubes.')

(b.) Calculate the second derivative of ()=cos (ln(² +1).

(c.) Using the definition of the inverse function, differentiate ()=tan^-1 (2).

2.Consider the function ()= (5+ ²)/(2+² ) over the domain [0,5].

(a.) Sketch the function.

(b.) Calculate the absolute maximum and absolute minimum of ().

3. Consider a curve defined parametrically as ()= 21/t and ()=2+1/t.

(a.) Write the equation in non-parametric form (i.e. eliminate t between the equations.)

(b.) Find ²y/x² in terms of t using parametric differentiation.

(c.) Find /xin terms of t using parametric differentiation.

(d.) Find the equation of the tangent line to the curve when t = 1. |