Math Help - Implicit Differentiation

1. Implicit Differentiation

Find dydx in terms of x and y if arcsin((x^5)(y))=(x)(y^5)

I tried to do this problem, and I got (y^5((1-(x^5y)^2))^(1/2)-(5yx^4))/(x^5-5xy^4(((1-x^5y)^2))^(1/2)), which is incorrect.

2. Originally Posted by iheartthemusic29
Find dydx in terms of x and y if arcsin((x^5)(y))=(x)(y^5)

I tried to do this problem, and I got (y^5((1-(x^5y)^2))^(1/2)-(5yx^4))/(x^5-5xy^4(((1-x^5y)^2))^(1/2)), which is incorrect.

$Arcsin\, (x^5y)=xy^5 \Longrightarrow \frac{5x^4y}{\sqrt{1-x^{10}y^2}}\,dx+\frac{x^5}{\sqrt{1-x^{10}y^2}}\,dy=y^5\,dx+5xy^4\,dy$