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7. * 10110 Use the given values to compute the derivatives. (a) (-/10) Given f(5) = 2, f'(5) 7. Calculate F'(5), where F(:L') : 3:2f(:c) (b) (-/10) Given f(2) = 5,f'(2) : 7,g(2) = 2,g'(2) : 3. Calculate H'(2), where Hm = assign) 8. In this problem, we'll compute the derivative d $27: + 5 dt t2 3:): Since the derivative is with respect tot (because of the dt in the denominator), the a: in this function is actually just a constant. (a) Keeping in mind that :L' is a constant, what is the derivative with respect to t of the denominator t2 33:? (b) What is the derivative of the numerator 332t + 5, again remembering that :c is a con- stant? (Hint: What is the derivative ont? What is the derivative 0f5t? What is the derivative of17t? What is the derivative ofanything oftheform (constant) - t?) (c) Now use the Quotient Rule to nish computing the derivative. 9. Calculate the rst, second, and third derivatives of f (a) f(t) : 31:3 3t2 + 1 (b) f(x) = 6/5 (fourth root of it) (c) f(t) = 5752 + Enst 10. * (/20) Find the equation of the tangent line to the function g(:c) at :1: = 1. Where g(:c) = f'($) and f($) = 8933 + 3.132 + 533. 11. * (/20) Calculate following derivatives: (a) %, where f(t) = 16ttan(t) (b) f'(33), where f(g;) = 7x sin(m)+6