Question

Find the derivative of the function.
y=sqrt( 3x+sqrt( 3x+sqrt( 3x)))

Answer 1

nested radical function... you have to use chain rule

let me try to simplify it using substituted functions
\[u = \sqrt{3x} \rightarrow du = \frac{3}{2 \sqrt{3x}}\]
\[v = \sqrt{3x + \sqrt{3x}} = \sqrt{3x +u}\]
\[\rightarrow dv = \frac{3 + du}{2 \sqrt{3x+u}}\]
\[y = \sqrt{3x +v} \rightarrow dy = \frac{3 + dv}{2 \sqrt{3x +v}}\]

now you have dy, just substitute everything in