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 `

If y=f(x^(3)),z=g(x^(2)),f'(x),=cosx and g'(x)=sinx," then "(dy)/(dz) is

If u=f(x^2), v=g(x^3) , f'(x)=sinx and g'(x)= cos x then find (du) / (dv) .

If x= f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2 (a) f(t)-f^(primeprime)(t) (b) {f(t)-f^(primeprime)(t)}^2 (c) {f(t)+f^(primeprime)(t)}^2 (d) none of these

If f(x)=|x-2|a n dg(x)=f[f(x)],t h e ng^(prime)(x)= ______ for x>20

Suppose that f(x) is differentiable invertible function f^(prime)(x)!=0a n dh^(prime)(x)=f(x)dot Given that f(1)=f^(prime)(1)=1,h(1)=0 and g(x) is inverse of f(x) . Let G(x)=x^2g(x)-x h(g(x))AAx in Rdot Which of the following is/are correct? G^(prime)(1)=2 b. G^(prime)(1)=3 c. G^(1)=2 d. G^(1)=3

let f(x)=e^(x),g(x)=sin^(-1)x and h(x)=f(g(x)) th e n fin d (h'(x))/(h(x))

f_(n)(x)=e^(f_(n-1)(x))" for all "n in N and f_(0)(x)=x," then "(d)/(dx){f_(n)(x)} is

Let the function f satisfies f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) foe all x and f(0)=3 The value of f(x).f^(prime)(-x)=f(-x).f^(prime)(x) for all x, is

If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove that varphi(x)=|f(x)g(x)h(x)f^(prime)(x)g^(prime)(x)h^(prime)(x)f^(x)g^(x)h^(x)|i sacon s t a n tpol y nom i a l

Let g^(prime)(x)>0a n df^(prime)(x)<0AAx in Rdot Then (f(x+1))>g(f(x-1)) f(g(x-1))>f(g(x+1)) g(f(x+1))