xy+2x+3x^2 = 4

Posted by andi telaumbanua on Feb 11, 2018 in Matematika |
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Carilah y^’ dari fungsi xy+2x+3x^2=4 !

Jawab :

Gunakan metode turunan implisit

xy+2x+3x^2=4

y = (4-2x-3x^2)/x

maka:

(d (xy+2x+3x^2 ))/dx = (d(4))/dx

(d( xy))/dx+ d( 2x )/dx+ (d(3x^2))/dx = (d( 4))/dx

[(d( x)/dx)(y)+ (x)(d(y)/dx) ]+ d( 2x )/dx+ (d(3x^2))/dx = (d( 4))/dx

y+x d(y)/dx+ 2+ 6x = 0

x d(y)/dx= -(y+2+6x)

dy/dx=-(y+2+6x)/x

maka∶

dy/dx=(-((4-2x-3x^2)/x)-2-6x)/x

dy/dx=((-((4-2x-3x^2)/x)-2-6x)/x) (x/x)

dy/dx=(-4+2x+3x^2-2x-6x^2)/x^2

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

for more detailed writing click on the following link Carilah y^’ dari fungsi xy+2x+3x^2=4 !

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