Tentukanlah turunan pertama dari: x^3 y-5x^2 y^2 log⁡(xy)+y^3=3

Posted by andi telaumbanua on Jul 29, 2018 in Matematika |
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Tentukanlah turunan pertama dari:
x^3 y-5x^2 y^2 log⁡(xy)+y^3=3

Jawab:
d/dx(x^3 y) – d/dx (5x^2 y^2 ) + d/dx [log⁡(xy)] + d/dx(y^3)=d/dx(3)

3x^2 y+ x^3 dy/dx -10xy^2 – 10x^2 y dy/dx + y/(xy ln⁡10 ) + (x/(xy ln⁡10 )) dy/dx+3y^2 dy/dx = 0

x^3 dy/dx-10x^2 y dy/dx + (x/(xy ln⁡10 )) dy/dx + 3y^2 dy/dx = 10xy^2-3x^2 y-y/(xy ln⁡10 )

dy/dx (x^3-10x^2 y+x/(xy ln⁡10 )+3y^2)= 10xy^2-3x^2 y-y/(xy ln⁡10

dy/dx =(10xy^2-3x^2 y-y/(xy ln⁡10 ))/(x^3-10x^2 y+x/(xy ln⁡10 )+3y^2 )

dy/dx=[(10xy^2-3x^2 y-1)/(x ln⁡10 )] / [(x^3-10x^2 y+1/(y ln⁡10 )+3y^2 ]

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