Question

y=x*sqrt(2-x^3) , find y'

Answer 1

\[f(x) = y=x*\sqrt{2-x^3}\]

Product rule and chain rule.

\[1\sqrt{2-x^3}\ + \frac{-3x^2}{2\sqrt{2-x^3}} * x\]

So..

\[\frac{2(2-x^3) - 3x^3}{2\sqrt{2-x^3}}\]

Which is

\[\frac{4-2x^3 - 3x^3}{2\sqrt{2-x^3}}\]

Soooo...

\[\frac{4 - 5x^3}{2\sqrt{2-x^3}}\]

Answer 2

Thanks!