<jupyter_start><jupyter_text>b) y + ey - x = 2 dy/dx = 1 / (1 - ey)A derivada não pode ocorrer em zeroO resultado da função é em um plano tridmensional<jupyter_code>fig = plt.figure()
ax = plt.axes(projection="3d")
    
def funcao_z(x, y):
    return y + e**y - x - 2
    
x = np.linspace(-6, 6, 30)
y = np.linspace(-6, 6, 30)
    
X, Y = np.meshgrid(x, y)
Z = funcao_z(X, Y)
    
ax.plot_wireframe(X, Y, Z, color='green')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
    
ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
                    cmap='viridis', edgecolor='none')
ax.set_title('Gráfico de b');
    
plt.show()
def derivada_b (y):
    if y !=0:
        return 1 / (1 - e**y)
y = [-6]
dydx = [derivada_b(y[-1])]
h = 0.1
while y[-1] < -0.5:
    y.append(y[-1]+h)
    dydx.append(derivada_b(y[-1]))
plt.subplot(1,2,1)
plt.plot(y, dydx)
y = [0.5]
dydx = [derivada_b(y[-1])]
while y[-1] < 6:
    y.append(y[-1]+h)
    dydx.append(derivada_b(y[-1]))
plt.subplot(1,2,2)
plt.plot(y, dydx)<jupyter_output><empty_output><jupyter_text>c) (x2 + y2)3/2 = 10xy dy/dx = (3x(x2  + y2) - 10y) / (10x -3y(x2  + y2))Os resultados da função e da derivada são dados em um plano tridmensional<jupyter_code>fig = plt.figure()
ax = plt.axes(projection="3d")
    
def funcao_z(x, y):
    return (x**2 + y**2)**(3/2) - 10*x*y
    
x = np.linspace(-6, 6, 30)
y = np.linspace(-6, 6, 30)
    
X, Y = np.meshgrid(x, y)
Z = funcao_z(X, Y)

ax.plot_wireframe(X, Y, Z, color='green')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
    
ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
                    cmap='viridis', edgecolor='none')
ax.set_title('Gráfico de c');
    
plt.show()
fig = plt.figure()
ax = plt.axes(projection="3d")

def derivada(x, y):
    return ( (3*x*( (x**2 + y**2)**(1/2)) ) - (10*y) ) / ( (10*x)-( 3*y*( (x**2 + y**2)**(1/2)) ) )
    
x = np.linspace(-6, 6, 30)
y = np.linspace(-6, 6, 30)
    
X, Y = np.meshgrid(x, y)
Z = derivada(X, Y)

ax.plot_wireframe(X, Y, Z, color='green')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
    
ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
                    cmap='viridis', edgecolor='none')
ax.set_title('Gráfico da derivada de c');
    
plt.show()<jupyter_output><empty_output>
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