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asdf12312
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Homework Statement
Use the IMPLICIT FUNCTION THEOREM (and not implicit differentiation) to find dy/dx at the point (1,1) when
y^5 + x^2*y^3 − y*e^(x^2) = 1.
Homework Equations
f(x,y)=0
dy/dx = - [f(x)/f(y)] = -[d/dx(f(x,y) / d/dy(f(x,y)]
The Attempt at a Solution
solving for f(x,y), i brought the 1 to the left side so the equation equaled 0, i.e y^5 + x^2*y^3 − y*e^(x^2)-1=0
then d/dx of the function I got 2xy^3 - 2xye^(x^2)
d/dy = 5y^4 + 3x^2y^2 - e^(x^2)
so dy/dx was just -[d/dx / d/dy] = -[2xy^3 - 2xye^(x^2) / 5y^4 + 3x^2y^2 - e^(x^2)]
for the point (1,1) i just plugged in x and y into the above equation, and got 0.65 as my answer.
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