Question

Find d2y/dx^2, in terms of x and y for the equation y^2=x^3

Answer 1

first you need y'

Answer 2

\[2yy'=3x^2\]

Answer 3

or
\[y'=\frac{3x^2}{2y}\] now again, this time with quotient rule

Answer 4

constants getting on my nerves. lets write it as
\[\frac{3}{2}\frac{x^2}{y}\] and take the derivative of second part. you get
\[y''=\frac{2}{3}\frac{2xy-x^2y'}{y^2}\] so far so good?

Answer 5

now replace
\[y'\] by
\[\frac{3x^2}{2y}\] and do some annoying algebra to get your answer

Answer 6

\[\frac{2}{3}\frac{2xy-x^2\times \frac{3x^2}{2y}}{y^2}\] multiply top and bottom by 2y to clear the fraction get
\[\frac{2}{3}\frac{4xy^2-3x^4}{2y^3}\] check my algebra because i am typing not writing.

Answer 7

now don't forget that
\[y^2=x^3\] so you can replace all y squares you see by x cubed and simplify more

Answer 8

yo satellite please help me when you're done here

Answer 9

guess i am done