Question

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Consider a ‘Witch of Agnesi’ curve, defined:
x^2 y + 4y = 8
Find:
a) dy/dx as a function of x, using implicit differentiation. Then, verify your result by finding y explicitly and differentiating.

b) The equation of the tangent line to the graph when x = 2.

Answer 1

The answers are as follow:

a) y'= -2x/y

b) y' = -4/y

Why do we use implicit differentiation?

The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y.

Given:

x²y+4y=8

On differentiation

applying product rule

2xy+ x²y'  = 0

2xy = - x²y'  

2y = -xy'

y'= -2x/y

b) equation of the tangent line to the graph when x = 2.

y' = -4/y

Learn more about implicit differentiation here:

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