Turunan kedua dari x^4+ y^4 = 81

Posted by andi telaumbanua on Feb 11, 2018 in Matematika |
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Carilah y^” dari fungsi x^4+ y^4 = 81 !

Jawab :

Gunakan metode turunan implisit

(d(x^4))/dx + (d(y^4))/dx= ((d(81))/dx

4x^3+(d(y^4 )/dy)(dy/dx )=0

4x^3+ 4y^3 y^’=0

y^’= -x^3/y^3

Maka :

y^”= -((d(x^3 )/dx)(y^3 )-x^3 (d(y^3 )/dx) )/(y^3)^2

y^”= -(3x^2 (y^3 )-x^3 (3y^2 )(y^’))/y^6

y^”= -(3x^2 y^3-x^3 (3y^2 )(-x^3/y^3 ))/y^6

y^”= -(3x^2 y^3+ 3x^6/y)/y^6

y^”=(-(3x^2 y^3+ 3x^6/y)/y^6 )(y/y)

y^”= -(3(x^2 y^4+ x^6) )/y^7

y^”= -(3x^2 (y^4+ x^4) )/y^7

Atau

y^”= -(3x^2 (81) )/y^7 = -243(x^2/y^7 )

for more detailed writing click on the following link Carilah y^” dari fungsi x^4+ y^4 = 81 !

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