implicit differentiation

Question

2x+3x^2+1=y^2

Please explain each step in detail. Thank you!

Answer 1

2x + 3x² + 1 = y²

Take the derivative of each term with respect to "x":

The derivative of 2x (with respect to "x") is 2

The derivative of 3x² (with respect to "x") is 6x

The derivative of 1 (with respect to "x") is 0

The derivative of y² (with respect to "x") is (using the chain rule) 2y•y'

So, putting these all together we get:

2 + 6x + 0 = 2y•y'

(2 + 6x) = 2y•y'

2(1 + 3x) = 2y•y'

2(1 + 3x)/2y = y'

(1 + 3x)/y = y'

y' = (3x + 1)/y