Question

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?

Answer 1

This is just explicit differentiation

Answer 2

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

Answer 3

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

Answer 4

or rather y is a function

Answer 5

so for your problem,

x^(1/3) = 5(y)^(1/2)

take the derivative of both sides

and solve for y'

Answer 6

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

Answer 7

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/implicitdiffdirectory/ImplicitDiff.html

Answer 8

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

Answer 9

you took the derivative incorrectly,

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