If (5 x^2)+ 3 x + xy = 5 and y( 5 ) = −27, find y′( 5 ) by implicit differentiation.. Created by k. science-mathematics-en - mathematics-en

If (5 x^2)+ 3 x + xy = 5 and y( 5 ) = −27, find y′( 5 ) by implicit differentiation.?

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If (5 x^2)+ 3 x + xy = 5 and y( 5 ) = −27, find y′( 5 ) by implicit differentiation.?

If (5 x^2)+ 3 x + xy = 5 and y( 5 ) = −27, find y′( 5 ) by implicit differentiation.

5x^2+3x+xy=5

Differentiate:

10x+3+xy'+y=0

xy'=-10x -y-3

y'= (-10x-y-3)/x

y'(5)= (-10(5)-(-27)-3)/5

y'(5)= (-50+27-3)/5

y'(5)= -26/5

Should be right, someone should check my work however.

dy/dx =

10x +3 + xdy/dx + y = 0

(10x + y + 3)/x = dy/dx

dy/dx = (y+3)/x + 10

you now have sufficient information to do the calculation