Calculus Help Please!!!
posted by Josh on .
Use implicit diff. to find dy/dx of each of the following. In the following x,y and (a) are all variables. Show step by step please! Thank you!
1) y^2 = x^2+a^2
2) y^2+ay = x^2+ax+a^2

2 y dy/dx = 2 x + 2 a da/dx
y dy/dx = (x+a da/dx)
dy/dx = (x + a da/dx)/y
or
dy/dx = (x + a da/dx)/(x^2+a^2)^.5

2 y dy/dx + a dy/dx + y da/dx = 2 x^2 + a + x da/dx + 2 a da/dx
(2y+a)dy/dx = 2 x^2 +a +(xy+2a)da/dx
dy/dx = [2 x^2 +a +(xy+2a)da/dx]/(2y+a) 
I suspect in each, a is a constant, so da/dx=0

I figured the same but he said specifically that a was variable.

My answers were like these
1)
2yy'=2x+2a
y'=2x+2a/2y
2)
2yy'+ay'+y=2x+a+x+2ay
2yy'+ay'=3x+3ay
y'(2y+a)=3x+3ay
y'=3x+3ay/2y+a
And my teacher said I made mistakes with my answers but I couldn't figure out.