Calcular la derivada implícita dy / dx : 7x ^ 3 y ^ 2 + 5y ^ 2 + 3x = x ^ 2 + y?

D / d

x (

7

x ^ 3

y ^

2 +

5

y ^ 2 +

3

x

) = d / d

x (

x ^ 2 +

y

)d / dx [7x ^ 3y ^ 2] + d / dx [5y ^ 2] + d / dx [3x]Evalue d / dx [7x ^ 3y ^ 2]7 (2x ^ 3y d / dx [y] + 3y ^ 2x ^ 2) + d / dx [5y ^ 2] + d / dx [3x]evalue d / dx [5y ^ 2]7 (2x ^ 3y d / dx [y] + 3y ^ 2x ^ 2) + 10y d / dx [y] + d / dx [3x]Evalue d / dx [3x]7 (2x ^ 3y d / dx [y] + 3y ^ 2x ^ 2) + 10y d / dx [y] + 3xsimplifica14x ^ 3y d / dx [y] + 21x ^ 2y ^ 2 + 10y d / dx [y] + 32x + d / x [y]14x ^ 3 yy' + 21x ^ 2y ^ 2 + 10yy' + 3 = 2x + y'y' = - 21x ^ 2y ^ 2 - 2x + 3 / 14x ^ 3y + 10y - 1remplace y' con dy / dx = 21x ^ 2y ^ 2 - 2x + 3 / 14x ^ 3y + 10y - 1.