1/x+ 1/y = 1

Posted by andi telaumbanua on Feb 11, 2018 in Matematika |
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Carilah y^’ dari fungsi 1/x+1/y=1!

Jawab : Gunakan metode turunan implisit

1/x+1/y=1

y = x/(x-1)

maka:

(d (1/x+1/y ))/dx = (d(1))/dx

(d(1/x ))/dx+ d(1/y )/dx = (d( 1))/dx

(((0)(x)- (1)(1))/x^2 )+ (((0)(y)-(1)(dy/dx))/y^2 )=0

-1/x^2 – (dy/dx)/y^2 =0

dy/dx= -y^2/x^2

maka:

dy/dx= -(x/(x-1))^2/x^2

dy/dx= -(x^2/(x^2-2x+1))/x^2

dy/dx= -x^2/(x^4-2x^3+ x^2 )

for more detailed writing click on the following link Carilah y^’ dari fungsi 1/x+1/y=1

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