If `u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v)` is (a) `3/2xcosx^3cos e cx^2` (b) `2/3sinx^3secx^2` (c) `tanx` (d) none of these

If y=f(x)=x^3+x^5 and g is the inverse of f find g^(prime)(2)

If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ((dx)/(dt))^2+((dy)/(dt))^2= f(t)-f"(t) (b) {f(t)-f"(t)}^2 (c) {f(t)+f"(t)}^2 (d) none of these

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real xdot Then g^(f(x)) equals. -(f^(x))/((f^'(x))^3) (b) (f^(prime)(x)f^(x)-(f^(prime)(x))^3)/(f^(prime)(x)) (f^(prime)(x)f^(x)-(f^(prime)(x))^2)/((f^(prime)(x))^2) (d) none of these

Prove that (2cos^3x-cosx)/(sinx - 2sin^3x) = cotx

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

If Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1+x),e^(x),sinx),(cosx,tanx,sin^(2)x):}| then

If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in this interval

Prove that (cos^3x - sin^3x)/(cosx - sinx) = (2 + sin2x)/2

If f(x)=x+tanx and g(x) is the inverse of f(x) , then differentiation of g(x) is (a) 1/(1+[g(x)-x]^2) (b) 1/(2-[g(x)+x]^2) (c)1/(2+[g(x)-x]^2) (d) none of these

f(x)=sinx+cosx+3 . find the range of f(x).