Calculus Implicit DifferentiationI’m trying to find an equation for the line tangent to the graph of ln y +

Question

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 3×2 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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