If `f^(prime)(x^2)=(lnx)/(x^2)andf(1)=-1/4,t h e n(A)f(e)=0(B)f^(prime)(e)=1/20`

f'(x^(2))=(ln x)/(x^(2)) and f(1)=-(1)/(4), then (A)f(e)=0(B)f'(e)=(1)/(20)

If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is (a)2 (b) 1 (c) -2 (d) none of these

If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is (a)2 (b) 1 (c) -2 (d) none of these

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

If f(1)=3,f^(prime)(1)=2,f^(1)=4,t h e n(f^(-1))^()(3)= a. 1 b. -1/2 c. -2 d. none of these

If f(1)=3,f^(prime)(1)=2,f^(1)=4,t h e n(f^(-1))^(' ')(3)= a. 1 b. -1/2 c. -2 d. none of these

If f(1)=3,f^(prime)(1)=2,f ^(' ')(1)=4,t h e n(f^(-1))^(' ')(3)= a. 1 b. -1/2 c. -2 d. none of these

A function f: Rvec[1,oo) satisfies the equation f(x y)=f(x)f(y)-f(x)-f(y)+2. If differentiable on R-{0}a n df(2)=5,f^(prime)(x)=(f(x)-1)/xdotlambdat h e nlambda= 2^(prime)f(1) b. 3f^(prime)(1) c. 1/2f^(prime)(1) d. f^(prime)(1)

A function f: Rvec[1,oo) satisfies the equation f(x y)=f(x)f(y)-f(x)-f(y)+2. If differentiable on R-{0}a n df(2)=5,f^(prime)(x)=(f(x)-1)/xdotlambdat h e nlambda= 2^(prime)f(1) b. 3f^(prime)(1) c. 1/2f^(prime)(1) d. f^(prime)(1)

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a)f^(prime)(x)=f(x)=0 (b)4f^(x)+f(x)=0 (c)f^(x)+f(x)=0 (d)4f^(x)-f(x)=0