Question

this chain rule problem is a bit confusing. x(2x-3)^1/2

Answer 1

3(x-1)/(2x-3)^-.5

Answer 2

\[[x(2x-3)^\frac{1}{2}]'= \text{ (apply product rule ) }[x]'(2x-3)^\frac{1}{2}+x[(2x-3)^\frac{1}{2}]'\]

Answer 3

\[[x]'=1\]
\[[(2x-3)^\frac{1}{2}]'=\frac{1}{2}(2x-3)^{\frac{1}{2}-1}(2)\]

Answer 4

\[[x(2x-3)^\frac{1}{2}]'=(2x-3)^\frac{1}{2}+x(2x-3)^\frac{-1}{2}\]

Answer 5

\[(2x-3)^\frac{1}{2}+\frac{x}{(2x-3)^\frac{1}{2}}\]

Answer 6

\[(2x-3)^\frac{1}{2} \cdot \frac{(2x-3)^\frac{1}{2}}{(2x-3)^\frac{1}{2}}+\frac{x}{(2x-3)^\frac{1}{2}}\]

Answer 7

\[\frac{(2x-3)+x}{(2x-3)^\frac{1}{2}}\]

Answer 8

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

Answer 9

\[\frac{3(x-1)}{\sqrt{2x-3}}\]