Answer to Question #239255 in Calculus for CELL

Question

Use chain rule to find the derivative and express the final answer in terms of x in radical form of

y= u^1/2 and u= x^1/2

Answer 1

Let us use the chain rule $y'_x=y'_uu'_x:$

$y'_x=\frac{1}2u^{-\frac{1}2}\frac{1}2x^{-\frac{1}2}= \frac{1}4(x^{\frac{1}2})^{-\frac{1}2}x^{-\frac{1}2}$

$=\frac{1}4x^{-\frac{1}4}x^{-\frac{1}2} =\frac{1}4x^{-\frac{3}4}=\frac{1}{4\sqrt[4]{x^3}}.$