Question

Derivada de:
x^3 y^3 + tg (xy) = 2x + y^2 -10

Es una derivada implicita porfavor con pasooos

Answer 1

$\#0: \; x^3 y^3 + \tan (xy) = 2x + y^2 -10\\ \\ \#1: \; \left[x^3 y^3 + \tan (xy)\right]' = (2x + y^2 -10)'\\ \\ \#2: \; (x^3 y^3)' + [\tan (xy)]' = (2x)' + (y^2)' - (10)'\\ \\ \#3: \; [(x^3)' y^3+x^3(y^3)'] + \sec^2 (xy)\cdot (xy)' = 2 + 2yy'\\ \\ \#4: \; 3x^2y^3+3x^3y^2y'+ \sec^2 (xy)\cdot (y+xy')= 2 + 2yy'\\ \\ \#5: \; 3x^2y^3+y\sec^2 (xy)-2=2yy'-3x^3y^2y'-y'\sec^2 (xy)\\ \\ \\ \#6: \; y'=\dfrac{3x^2y^3+y\sec^2 (xy)-2}{2y-3x^3y^2-\sec^2 (xy)}$