show work please

(Show your work to get full credit) 1. (20%) Differentiate the function y = J}? +in(5 ) . 2. (20%) Use implicit differentiation to find an equation of the line tangent to the curve 1 1 + = 2, at the point (-2.1)- 2x + 3 2 y 3 3. (20%) Suppose we know that the radius of a circle is increasing at a rate of 8 feet each second (Fig. 1), and we want to know how fast the area of the circle is increasing when the radius is 5 feet. What can we do? Fig. l 4. (20%) Find a root of f(x) = x3 e", by Newton's method, within the accuracy of 0.1. You can use the following table to show your calculations f'(x) " f'(x) - 5. (20%) Express the derivative 6% in terms of x, if y = u(1+u2)3 and u = (3x 2)2