Can you explain it to me after you solve it thank you?.

(10 points) Air is being pumped into a spherical balloon so that its volume increases at a rate of 2 cm3/seconds. How fast is the radius of the balloon increasing when the diameter is 6 cm (in exact value and in terms of n)? (Hint: Volume of a sphere = =mr3, where r is the radius of the sphere.) 5) 2 6. (6 points) Find the linear approximation L(x) to y = f (x) near x = a for this function [Hint: L(x) = f(a) + f'(a)(x - a)]: f(x) = Vx+3 at a=13. (10 points) Find all numbers c (in exact value) that satisfy the conclusion of the Mean Value Theorem for f(x) = x3 - X over [0, 2]: (Hint: The Mean Value Theorem f'(c) = (@ b-a over the given interval [a, b]): 3) 4. (10 points) Use logarithmic differentiation to find ay: dx y = (3x4 - 2) tanx7. (16 points) For the given equation: xy' + cos(my) - 2x2 = 9 a) Use implicit differentiation to find dy dx 7a) b) Find the equation of the tangent line to the given equation at point (2, -3): 7b) 8. (10 points) Differentiate the following: ne- ne-x V= extex