calculus
posted by Kim on .
Alright so implicit differentiation is just not working out for me.
Use implicit differentiation to find the slope of the tangent line to the curve at point (4,1).
y / (x2y) = x^3 + 4
Tried quotient rule to get the derivative of the left side, then got derivative of right side, and ultimately I got y + 3x^2 (x2y)^2 / x2y2y
This is clearly not correct since the bottom would turn into zero if I plugged in x and y. Sigh...

It will be easier if you multiply it out and combine terms.
9y = x^4 +4x 2x^3 y
Differentiate both sides with respect to x implicitly, treating y as a function of x.
9 dy/dx = 4x^3 + 4 2x^3 dy/dx
6x^2 y
dy/dx(9 + 2x^3) = 4x^3 + 4  6x^2 y
dy/dx = [4x^3 6x^2 y +4]/(9 + 2x^3)
Plug in x=4 and y=1. You should not get a zero deniminator.