1.Find the set of Points where the function of f(x)=tan[∏²]x-tan[-∏^2]x

2. If 5f(x)+3f(1/x)=x+2 and y=xf(x), then dy/dx at x=1

3. Let a real function f is given by f(x) =n(x^1/n-1), x>0. If f(x) satisfies 97f(1/x)+Kf(x)=0, then find the value of K

If 5f(x)+3f(1/x)=x+2 and y=xf(x), then dy/dx at x=1

5f(x)+3f(1/x)=x+2

25f(x)+15(1/x)=5x+10…………………..(i)

Replacing x with 1/x,

5f(1/x)+3(x)=1/x+2

15f(1/x)+9f(x)=3/x+6………………………(ii)

(i)-(ii)

16f(x)=5x-3/x+4

f(x)=5x/16-3/16x+1/4

y=xf(x)=5x²/16-3/16+x/4

dy/dx=10x/16+1/4

dy/dx at x=1 is 10/16+1/4=7/8