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Mathematics 33 Online
OpenStudy (anonymous):

Implicit differentiation, equation to follow

OpenStudy (anonymous):

\[\sqrt{x}+\sqrt{y}=5\]

OpenStudy (anonymous):

Would this just be \[x^1/2+y^1/2=\]

OpenStudy (heisenberg):

what are you attempting to derive?

OpenStudy (anonymous):

i am trying to find dy/dx of the above equation

OpenStudy (heisenberg):

it's been a while so i may be fuzzy, but the basic gist is: 1. Since we are doing dy/dx, treat all 'x's as constant and take the derivative. 2. When you derive a 'y' term, also include a dy/dx 3. solve for dy/dx

OpenStudy (heisenberg):

so i THINK: \[x^\frac{1}{2} + \frac{1}{2}*y^\frac{-1}{2}*\frac{dy}{dx} = 0\]

OpenStudy (heisenberg):

\[\frac{dy}{dx} = - 2 * \sqrt y * \sqrt x\]

OpenStudy (anonymous):

Think you are mixing up you partial differentiation with your single variable calculus

OpenStudy (anonymous):

In single variable cal, you differentiate the x also

OpenStudy (anonymous):

so would the fourmula be\[x+dy/dx+y+dy/dx\]

OpenStudy (heisenberg):

i don't know that you have to use implicit differentiation to solve this actually. can't you just solve for y and then derive?

OpenStudy (anonymous):

start from the top. Differentiate each item; the y item you write in dy/dx next to it. Solve for dy/dx. There is no formula per se zbay. You differentiate and then solve for dy/dx

OpenStudy (anonymous):

ok thanks let me attempt to work it out

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