5. Calcular as derivadas parciais de primeira ordem das seguintes funções: a) f(x, y) = xy3 − x2y b) f(x, y) = xy/(x2 + y2) c) f(x, y) = sen(x2) s...

a) f(x, y) = xy3 − x2y fx = y^3 - 2xy fy = 3xy^2 - x^2 b) f(x, y) = xy/(x2 + y2) fx = y/(x^2 + y^2) - 2x*y^2/(x^2 + y^2)^2 fy = x/(x^2 + y^2) - 2y*x^2/(x^2 + y^2)^2 c) f(x, y) = sen(x2) sen(√y) fx = 2x cos(x^2) sen(√y) fy = (1/2√y) cos(√y) sen(x^2) d) f(x, y) = sen(8x) cos(x2 + y2) fx = 8cos(8x) cos(x^2 + y^2) - 2x sen(8x) sen(x^2 + y^2) fy = -2y sen(8x) sen(x^2 + y^2) e) f(x, y) = √(sen(x2 + y2)) fx = cos(x^2 + y^2) * cos(x^2 + y^2)^(-1/2) * 2x fy = cos(x^2 + y^2) * cos(x^2 + y^2)^(-1/2) * 2y f) f(x, y) = cos(x2 + xy + y2) fx = -2x sen(x^2 + xy + y^2) + y cos(x^2 + xy + y^2) fy = -2y sen(x^2 + xy + y^2) + x cos(x^2 + xy + y^2) g) f(x, y) = e−(x2+y2) fx = -2x e^(-x^2-y^2) fy = -2y e^(-x^2-y^2) h) f(x, y) = ln(x+ y2) fx = 1/(x+y^2) fy = (2y)/(x+y^2)