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Mathematics 8 Online
OpenStudy (anonymous):

Find dy/dx in terms of x and y if x^(1/3) = 5sqrt(y) I don't understand this question. Is this supposed to be a simple derivative or is it different?

OpenStudy (australopithecus):

This is just explicit differentiation

OpenStudy (australopithecus):

You can just solve for y if you want then take the derivative, as dy/dx y is y' Or for example you can do this, dy/dx x^2 + y^2 = dy/dx 1 is 2x + 2yy' = 0 solve for y' y' = -2x/2y

OpenStudy (australopithecus):

when differentiating y you need to use chain rule on it, that is where y' comes from because y is the function itself

OpenStudy (australopithecus):

or rather y is a function

OpenStudy (australopithecus):

so for your problem, x^(1/3) = 5(y)^(1/2) take the derivative of both sides and solve for y'

OpenStudy (australopithecus):

Ignore this "You can just solve for y if you want then take the derivative, as dy/dx y is y'." best to just use the method I showed you

OpenStudy (anonymous):

so the answer is (1/3)x^(2/3)-( 5(1/2)y(-1/2) ) = dy/dx ?

OpenStudy (australopithecus):

you took the derivative incorrectly, Also you messed up the algebra, use y' do not use dy/dx

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