sin (x + y) = y^2 cos⁡ x

Posted by andi telaumbanua on Feb 11, 2018 in Matematika |
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Carilah dy/dx dari fungsi sin(x + y) = y^2 cos⁡x !

Jawab :

Gunakan metode turunan implisit

(d (sin(x + y) ))/dx = (d(y^2 cos⁡x ))/dx

cos (x + y) ((d(x+ y))/dx) = ((d(y^2))/dx)(cos⁡x)+(y^2 )((d(cos⁡x))/dx)

cos (x + y) [(d(x)/dx)+(dy/dx)]=(d(y^2 )/dy)(dy/dx)(cos⁡x)+ y^2 (- sin x)

cos (x + y) [ 1+dy/dx]=2y dy/dx(cos⁡x)- y^2 (sin x)

cos (x + y)+ dy/dx cos (x+y) =2y dy/dx(cos⁡x)- y^2 (sin x)

cos (x + y) + y^2 sin⁡x = 2y dy/dx cos⁡x – dy/dx cos (x+y)

cos (x + y) + y^2 sin⁡x = dy/dx[2y cos⁡x-cos ⁡(x+y) ]

dy/dx= (cos (x + y) + y^2 sin⁡x)/(2y cos⁡x-cos ⁡(x+y) )

for more detailed writing click on the following link Carilah dy/dx dari fungsi sin(x + y) = y^2 cos⁡x !

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