A few implicit differentiation problems

[number_13]

1.Use implicit differentiation to find the equation of the tangent line to the curve
xy^3+xy=16 at the point (8,1) . The equation of this tangent line can be written in the form y=mx+b

2.For the equation given below, evaluate y^1 at the point(1,-1) .
(6x-y)^4+2y^3=2399.

3.Find the equation of the tangent line to the curve (a lemniscate)
2(x^2+y^2)^2=25(x^2-y^2) at the point (3,-1). The equation of this tangent line can be written in the form y=mx+b

4.Find the slope of the tangent line to the curve sqrt(3x+3y)+sqrt(xy)=6.48 at the point
(1,5).

5.Use implicit differentiation to find the slope of the tangent line to the curve
y/(x+4y)=x^7+2 at the point (1,-3/11).

Anyone who can help... it would be greatly appreciated!

 

[rocomath]

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