Question

How do you find the derivative of `y =1/sqrt(x)`?

Answer 1

You could use the quotient rule or you could just manipulate the function to show its negative exponent so that you could then use the power rule.

I will convert the function to its negative exponent you make use of the power rule.

`y=1/sqrt(x)=x^(-1/2)`

Now bring down the exponent as a factor and multiply it by the current coefficient, which is 1, and decrement the current power by 1.

`y'= (-1/2)x^((-1/2 -1))=(-1/2)x^((-1/2-2/2))=(-1/2x^(-3/2))=-1/(2x^(3/2))`