Tentukan turunan pertama dari sin⁡(xy )+x^2=y^2+ 1

Posted by andi telaumbanua on Jul 28, 2018 in Matematika |
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Tentukan turunan pertama dari sin⁡(xy )+x^2=y^2+ 1

Jawab:

d/dx(sin(xy)+d/dx (x^2 )= d/dx (y^2 )+d/dx(1)

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(sin(xy)+ d/dx (x^2 )= d/dx (y^2 )+d/dx(1)

y cos⁡(xy)+x dy/dx cos⁡xy + 2x = 2y dy/dx + 0

x dy/dx cos⁡(xy)-2y dy/dx = -y cos⁡(xy)-2x

dy/dx (x cos⁡(xy)-2y)= -y cos⁡(xy)-2x

dy/dx = (-y cos⁡(xy)-2x)/(x cos⁡(xy)-2y)

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