y+sin⁡(xy)= 1 turunan pertamanya

Posted by andi telaumbanua on Feb 13, 2018 in Matematika |
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Tentukan turunan pertama dari bentuk implisit y+sin⁡(xy)= 1 !

Jawab :

Turunan bentuk implisit

Pertama kita turunkan dulu  sin⁡(xy)

Misalkan : u = xy

maka: du/dx=(1)(y)+ (x)(dy/dx)=y+x dy/dx

Maka: y = sin u

maka: dy/du=cos⁡ u=cos⁡(xy)

Sehingga :

dy/dx=(dy/du)(du/dx)

dy/dx=(cos⁡(xy) )(y+x dy/dx)

dy/dx= y cos⁡(xy) + x cos⁡(xy) dy/dx

Maka:

d[y+sin⁡(xy)]/dx = d(1)/dx

dy/dx + d(sin⁡(xy) )/dx=0

dy/dx + y cos⁡(xy)+ x cos⁡(xy) dy/dx=0

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

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


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