Question

If dy/dx = 2xy^2 , what is d^2y/dx^2 ?

Answer 1

To find d^2y/dx^2 (the second derivative of y concerning x), we need to differentiate dy/dx concerning x again using the product rule.

Step-by-step explanation:

To find d2y/dx2 (the second derivative of y concerning x), we need to differentiate dy/dx concerning x again. Using the product rule, we can differentiate 2xy2 as follows:

First, differentiate the term 2x, which gives us 2.

Next, differentiate the term y2. Using the power rule, we bring down the exponent and multiply by the derivative of y, which is dy/dx.

Putting it together, we get d2y/dx2 = 2 + 2y(dy/dx).

Answer 2

y'' = d^2 y / d x^2
= 2 ( x y' + y. 1 )
= 2x. y' + 2y
= 2x( 2 xy ) + 2y ...........from (1)
= 4 x^2 y + 2y
= 2y ( 2 x^2 + 1 )