Tentukan turunan pertama dari tan (xy) – 2y = 0

Posted by andi telaumbanua on Jul 28, 2018 in Matematika |
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Tentukan turunan pertama dari tan (xy) – 2y = 0

Jawab:

d/dx(tan(xy)-d/dx(2y)=d/dx(0)

Pertama Turunkan: d/dx(tan⁡(xy)

d/dx(tan⁡(xy)=[(1)(y)+ (x)(dy/dx)][sec^2⁡(xy)]

=(y+x dy/dx)(sec^2⁡ (xy)

=y sec^2⁡(xy) + x dy/dx sec^2⁡(xy)

Maka:
d/dx(tan(xy)-d/dx(2y)= d/dx()

y sec^2⁡(xy) + x dy/dx sec^2(⁡xy) -2 dy/dx = 0

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

dy/dx(x sec^2⁡(xy)-2) = -y sec^2⁡(xy)

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

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