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[answered] Calculus Implicit Differentiation I'm trying to find a


Calculus Implicit Differentiation

I'm trying to find an equation for the line tangent to the graph of ln y + x3 + 2xy = 10 at the point(2, 1) for a practice exam. Using Implicit Differentiation, I get a slope of -14/5. The solutions section says the slope should be -16/5. I believe the reason for this is that whoever created the solutions page accidentally plugged in 2 for y in the numerator after find what dy/dx equaled. Am I correct or am I missing something?


ln y x 3 2 xy 10

 

take derivative

 

1 dy

 

dy 3x2 2 y x 0

 

y dx

 

dx Put , x 2, y 1

 

1 dy

 

dy 3 22 2 1 2 0

 

1 dx

 

dx dy

 

dy 12 2 4

 

0

 

dx

 

dx

 

dy

 

5 14

 

dx

 

dy

 

14 dx

 

5

 


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