Question

Find d2y/dx2 in terms of x and y.
y^4 = x^5

Answer 1

y = \[y = \sqrt[4]{x^5} = x^{5/4}\]

Answer 2

well wouldn't you re-write the equation using index laws

\[y = x^{\frac{5}{4}}\]

so

\[y' = \frac{5}{4} x^{\frac{1}{4}}\]

then

\[y" = \frac{1}{4} \times \frac{5}{4} x^{-\frac{3}{4}}\]