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Solve the initial value problem for r as a vector function of t. dr Differential equation: dt = -7ti- 7t j - 3t k Initial condition: r(0) = 5i + j + 9k r(t) = it + kFind the derivative of the function at Po in the direction of A. f(x y) = - 3xy - 5y , Po(1, -1), A=i+5j (DAf) (1, - 1)= (Type an exact answer, using radicals as needed.)Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z) = (x/y) - yz, Po(- 3,1, - 1)Find the derivative of the function at Po in the direction of A. f(x, y,z) = xy + yz + zx, Po(2, -2, -3), A=2i+ 3j-6k (DAf) (2, -2, -3) = (Simplify your answer.)In which direction does the function increase most rapidly? 1= ) k (Type exact answers, using radicals as needed.) In which direction does the function decrease most rapidly? -1= (Type exact answers, using radicals as needed.) What is the value of the derivative in the direction of u? (Duf)Po (Type an exact answer, using radicals as needed.) What is the value of the derivative in the direction of - u? (D -uf)p.Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z) = (x/y) - yz, Po(-3,1, - 1)