Question

Find d2y/dx2 in terms of x and y.
y6 = x9

Answer 1

y^6 and X^9

Answer 2

are you supposed to find the second derivative of
\[y^6=x^9\]?

Answer 3

yes

Answer 4

ok here goes. the derivative of
\[x^9\] is
\[9x^8\] and the derivative of
\[y^6\] is
\[6y^5y'\] so first step is to write
\[6y^5y'=9x^8\]

Answer 5

solve for
\[y'\] to get
\[y'=\frac{3x^8}{2y^5}\]

Answer 6

clear so far, because that was the easy part

Answer 7

now you have to find \[y''\] using the quotient rule

Answer 8

yes

Answer 9

ok so the quotient rule: the denominator will be
\[4y^{10}\]

Answer 10

the numerator will be
\[2y^5\times 24x^7-3x^8\times 10y^4y'\] is that apart clear?