Question

Find the derivative of y=√x

Answer 1

$\frac{d \sqrt{x} }{ dx } = \frac{1}{2} \times {x}^{ \frac{1}{2} - 1} \\ = \frac{1}{ \sqrt{x} }$

Hope it will help you....

Answer 2

convert the square root to its exponential form and then use the power rule.

y =√x=x^{\frac{1}{2} }x21

Now bring the power of  1/2  down as a coefficient and then subtract 1 from the current power of 1/2  . Evaluate the fractions and simplify. Manipulate exponents from negative to positive.

y '=1 /2 x^(1/2−1 )

=1/2x ^(1/2 − 2/2)

= 1 /2 x^(−1/2)

= 1/ 2 x^(1/2 )

= 1 /2√x