Tentukan turunan pertama dari  x^2 sin ⁡(xy) + y = x

Posted by andi telaumbanua on Jul 28, 2018 in Matematika |
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Tentukan turunan pertama dari  x^2  sin⁡(xy)+ y=x

Jawab:

d/dx(x^2  sin(xy)+d/dx (y) = d/dx (x)

Pertama Turunkan: d/dx(sin⁡(xy)

d/dx(sin⁡(xy)=[ (1)(y)+ (x)(dy/dx)][cos⁡(xy)]

=(y+x dy/dx)(cos⁡(xy)

=y cos⁡(xy)+x dy/dx  cos(⁡xy)

Maka:

 

d/dx(x^2 sin(xy))+ d/dx (y)= d/dx (x)

2x(sin(xy))+x^2 (y cos⁡(xy)+ x dy/dx cos⁡(xy)+dy/dx =1

2x sin(xy)+x^2 ycos(xy)+x^3 dy/dx cos⁡(xy)+dy/dx = 1

dy/dx [x^3  cos⁡(xy)+1]= 1-2xsin(xy) – x^2 ycos(xy)

dy/dx = [1-2xsin(xy)-x^2 ycos(xy)]/[x^3  cos⁡(xy)+1]

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