Differentiate the functionand Radius

1. Differentiate the function y = 1. {x1 + 111(5):) . .I 2. Express the derivative 3 in tenns ofx if _}J=I(1+H1)3 and u = (3x 2):. 3. Use implicit differentiation to nd an equation ofthe line tangent to the curve 1 l + 2x+3 2y3 (Note: Using the implicit differentiation method is required. In fact, it is the easiest way;r to solve the problem.) = 2, at the point [-2.1]- 4. Suppose we know that the radius of a circle is increasing at a rate of 10 feet each seoond (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? Fltl 5. Use the format below to nd a root of f{x) = x3 e'x , by Newton's method, within the aocuracy of (1.1. m") [More rows if needed] Root is approximately