If 3x^2+3x+xy=4 and y(4)=−14,

find y'(4) by implicit differentiation.

3 answers

6 x dx + 3 dx + x dy +y dx = 0
(6 x + 3 + y ) dx + x dy = 0
x dy/dx = -( 6x + 3 + y)
at x = 4, y = -14
so at x = 4
4 dy/dx =- ( 24 + 3 - 14 ) = -13
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3x^2+3x+xy=4

In recrange Evaluate at (x0,y0) type 4 and -14

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You will see solution step-by-step
3x^2+3x+xy=4
dy/dx (3x^2+3x+xy) = dy/dx (4)
dy/dx (3x^2) + dy/dx (3x) + dy/dx (xy) = 0
6x+3+x(dy/dx)+y = 0
x(dy/dx) = -6x-3-y
dy/dx = (-6x-3-y)/x

y'(4) = (-6(4)-3-(-14))/(4)
y'(4) = (-24-3-(-14))/4
y'(4) = (-27+14)/4
y'(4) = -13/4