Question

How do you differentiate `y=sqrtx/(x^3+1)` using the quotient rule?

Answer 1

`(1-5x^3)/(2sqrtx(x^3+1)^2)`

Explanation:

`d/dx(f(x)/g(x))=(g(x)*d/dxf(x)-f(x)*d/dxg(x))/(g(x)^2)` ----------->(A)

here

f(x)=`sqrtx` and
g(x)= `x^3 +1`
`d/dx(sqrtx)=(1/(2*sqrt(x)))`
`d/dx(x^3+1)=3*x^2`

Substitute the above values in equation (A) and calculate the required answer.