differentiate y=cot^-12/x+tan^-1x/2

Question

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Answer 1

dy/dx=(-1/(1+4/x^2))(-2/x^2)+1/(2(1+x^2/4))=2/(x^2+4)+2/(x^2+4)=4/(x^2+4) (differentiation by parts)

The derivative of tan^-1(u)=1/(1+u^2); derivative of cot^-1(u)=-1/(1+u^2); derivative of 2/x=-2/x^2 and derivative of x/2=1/2. Differentiation by parts: dy/dx=dy/du * du/dx.