I need to find (dy/dx) for this problem "x^(1/2)+y^(1/2)=1" in two ways:
a) implicit differentiation, and
b) differentiating an explicit formula for y.
Thank you!
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I need to find (dy/dx) for this problem "x^(1/2)+y^(1/2)=1" in two ways:
a) implicit differentiation, and
b) differentiating an explicit formula for y.
Thank you!
First, to do the explicit diffentiation, rearrange the equation in the form y = f(x), and differentiate as normal. You should end up with dy/dx =f'(x), meaning it's a function of x only.
For implicit diffentiation, you set up the equation in the form F(x,y) = 0. In this case you have:
sqrt(x) + sqrt(y) -1 =0.
Differentiate with respect to x, and you get
which can be rearranged to give the answer as a function of both x and y.
Here's a site that works through a few problems that may be of help:
Visual Calculus - Implicit Differentiation
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