Derivada de:
x^3 y^3 + tg (xy) = 2x + y^2 -10
Es una derivada implicita porfavor con pasooos
x^3 y^3 + tg (xy) = 2x + y^2 -10
Es una derivada implicita porfavor con pasooos
CarlosMath
![\#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)}](https://tex.z-dn.net/?f=%5C%230%3A+%5C%3B++x%5E3+y%5E3+%2B+%5Ctan+%28xy%29+%3D+2x+%2B+y%5E2+-10%5C%5C+%5C%5C%0A%5C%231%3A+%5C%3B++%5Cleft%5Bx%5E3+y%5E3+%2B+%5Ctan+%28xy%29%5Cright%5D%27+%3D+%282x+%2B+y%5E2+-10%29%27%5C%5C+%5C%5C%0A%5C%232%3A+%5C%3B++%28x%5E3+y%5E3%29%27+%2B+%5B%5Ctan+%28xy%29%5D%27+%3D+%282x%29%27+%2B+%28y%5E2%29%27+-+%2810%29%27%5C%5C+%5C%5C%0A%5C%233%3A+%5C%3B++%5B%28x%5E3%29%27+y%5E3%2Bx%5E3%28y%5E3%29%27%5D+%2B+%5Csec%5E2+%28xy%29%5Ccdot+%28xy%29%27+%3D+2+%2B+2yy%27%5C%5C+%5C%5C%0A%5C%234%3A+%5C%3B++3x%5E2y%5E3%2B3x%5E3y%5E2y%27%2B+%5Csec%5E2+%28xy%29%5Ccdot+%28y%2Bxy%27%29%3D+2+%2B+2yy%27%5C%5C+%5C%5C%0A%5C%235%3A+%5C%3B+3x%5E2y%5E3%2By%5Csec%5E2+%28xy%29-2%3D2yy%27-3x%5E3y%5E2y%27-y%27%5Csec%5E2+%28xy%29%5C%5C+%5C%5C+%5C%5C%0A%5C%236%3A+%5C%3B+y%27%3D%5Cdfrac%7B3x%5E2y%5E3%2By%5Csec%5E2+%28xy%29-2%7D%7B2y-3x%5E3y%5E2-%5Csec%5E2+%28xy%29%7D "\#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)}")
1 votes
Thanks 0