Can somebody tell me if I'm right on this? The math looks right, yet it just feels so wrong due to the obscene steps I had to take to get it.
I hope I transcribed all that correctly from my paper.
- $y=\tan(xy^3)$
- $y'=\sec^2(xy^3)(y^3+3xy^2y')$
- $\frac{y'}{\sec^2(xy^3)}=y^3+3xy^2y'$
- $\frac{y'}{\sec^2(xy^3)}-3xy^2y'=y^3$
- $y'(\cos^2(xy^3)-3xy^2)=y^3$
- $y'=\frac{y^3}{\cos^2(xy^3)}$
Edited to substitute $\frac{1}{\sec^2(xy^3)}$ for $\cos^2(xy^3)$