Question

Differentiate the following function in respect to x: y=√x+1/√x ?

Answer 1

`dy/dx=-1/(2sqrt(x^3))`

Explanation:

`y=(sqrtx+1)/sqrtx`

`color(white)(y)=1+1/sqrtx=1+x^(-1/2)`

`"differentiate using the "color(blue)"power rule"`

`•color(white)(x)d/dx(ax^n)=nax^(n-1)`

`rArrdy/dx=-1/2x^(-3/2)=-1/(2x^(3/2))=-1/(2sqrt(x^3))`