Question

Differentiate y=sin^-1 [x/root (1+x^2)]

Answer 1

Question:-to differenitaiate y=sin^-1[x/(1+x)1/2]

Solution:-

Use the chain rule as well as quotient rule to differenitaiate it....

dy/dx={x/sin(1+x)^1/2}

dy/dx =[x'sin(1+x)^1/2-[{sin(1+x)}^1/2]'×x]/{(sin(1+x)^1/2}^2

dy/dx={1×sin(1+x)^1/2-1/2×sin(1+x)^-1/2×1×x}/{sin(1+x)}

dy/dx=[sin(1+x)^1/2-1/{2sin(1+x)^1/2)x]/sin(1+x)

dy/dx=[sin(1+x)^1/2-x/{2sin(1+x)^1/2}/sin(1+x)

This will be the required differenitaiation