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 y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a n dtany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) non of these

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If y=sqrt(log{sin((x^2)/3-1)}) , t h e n find (dy)/(dx)dot

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a) cospi/4 (b) sinpi/2 (c) sinpi/6 (d) cospi/3

If y=(1+x)(1+x^2)(1+x^4)......(1+x^(2n)), then find (dy)/(dx)a tx=0.