If y=sqrt(x)+1/sqrt(x), prove that 2x.dy/dx+y=2sqrt(x)

If y=sqrt(x)+1/sqrt(x), prove that 2x.dy/dx+y=2sqrt(x)

Problem

Question

If y=sqrt(x)+1/sqrt(x), prove that 2x.dy/dx+y=2sqrt(x)

Topic

Derivatives

Derivatives Problems

1. Find the derivative of e^x sinx+x^ncosx
2. Find the derivative of x/sinx
3. Differentiate sqrt((1-cos2x)/ (1+cos2x))
4. Differentiate f(x) =x^5 e^x+x^3 logx-2^x
5. Find the derivatives of (secx-1)(secx+1)
6. Find the derivatives of cos(x+a)
7. Find the derivative of f(x) =x cosx
8. Find the derivatives of cot^3x
9. Find the derivatives of (x^2+1) cosx
10. Find the derivative of 3^x+x^3+4x-6
11. Find the derivative of function y=1+x+x^2+…+x^50 at x=1
12. Find the derivatives of 2x^4+x
13. Find the derivative of f(x) =sinx+cosx /sinx-cosx
14. Find the derivatives of 5 secx+4cosx
15. If y=sqrt(x)+1/sqrt(x), prove that 2x.dy/dx+y=2sqrt(x)
16. Find f’(x) if f(x) =(x-2) ^2 (2x-3)
17. If y=sqrt(x/a) + sqrt(a/x), prove that (2xy) dy/dx=x/a-a/x