how would you solve (5xy^3=5)^2=x^2

Question

anonymous · Answer

That is typed exactly as it is shown in your book?

anonymous · Answer

oh sorry, it's (5xy^3+5)^2=x^2

anonymous · Answer

What do you have to solve for? There is only 1 equation and two unknowns so you won't be able to get a numerical answer

anonymous · Answer

$$(5xy^3+5)^2=x^2$$or$$(5xy^{3+5})^2=x^2$$first or second one?

anonymous · Answer

you have to use implicit differentiation to find the "y" prime in terms of x and y; the first one ( :

anonymous · Answer

The first thing I would do is get rid of the power of two by taking the square root of both sides. Makes it easier

anonymous · Answer

$$5xy^3+5=x$$

anonymous · Answer

$${d \over dx}[5xy^3+5=x]=5x2y^2y'+5y^3 + 0 = 1$$You have to do the product rule for the 5xy^3 term. Everytime you take the derivative of y you have to out a y' with it. The last steo is to just solve for y' algebraically

anonymous · Answer

Did that make sense?

anonymous · Answer

yes, that made sense. thank you so much . you saved

anonymous · Answer

Don't forget to simplify, the y;s should be able to reduce

anonymous · Answer

yes, yes i got it (: