please solve and explain

Calculus 1.5 Homework Differentiate each function with respect to .x. 1) v= (3x5 - 5)5 2) y= (-x* + 3)3 3) y = (5x2 + 1)-5 4) y = V2x2 + 3 For each problem, you are given a table containing some values of differentiable functions f(x) g(x) and their derivatives. Use the table data and the rules of differentiation to solve each problem. 5) " f (x) f' (x) 8 (x ) 8' (x ) Part 1) Given h (x) = (f(x)), find h (4) 1 2 1 4 -2 Part 2) Given h, (x) = f(g(x)), find h, '(4) 3 2 4 3 6) Given: y = f(x), with f(1) = 4, and f(1) = 3 7) If the derivative of y = k(x) is 2 when x = a. Find g'(1) if g(x) = Vf(x) 1, what is the derivative of b. Find h'(1) if h(x) = f( Vx) a. k(2x) when x = *Hint: apply the chain rule first, then plug in 1. b. k(x+1) when x = 0 *Hint: Apply the chain rule and plug in the given x value. 8. The graph of f and g are shown. 10 a. Find f(2) b. Find g(3) c. Find f '(2) (Hint: remember, derivatives are slopes) d. Find g'(4) e. g'(3) is undefined. Why do you think that is? f. Let h(x) = f(g(x)). Find h'(1) g. Let s(x) = g(f(x)). Find s'(9) 6 8 10