Home
Class 11
MATHS
Suppose fa n dg are functions having se...

Suppose `fa n dg` are functions having second derivative `f''` and `g' '` everywhere. If `f(x)dotg(x)=1` for all `xa n df^(prime)a n dg'` are never zero, then `(f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x))e q u a l` (a)`(-2f^(prime)(x))/f` (b) `(2g^(prime)(x))/(g(x))` (c)`(-f^(prime)(x))/(f(x))` (d) `(2f^(prime)(x))/(f(x))`

Promotional Banner

Similar Questions

Explore conceptually related problems

Let g^(prime)(x)>0a n df^(prime)(x) g(f(x-1)) f(g(x+1))>f(g(x-1)) g(f(x+1))

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

Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,

Using the first principle, prove that d/(dx)(1/(f(x)))=(-f^(prime)(x))/([f(x)]^2)

If f(x)=|x|^(|sinx|), then find f^(prime)(-pi/4)

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^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

If f(x-y),f(x)f(y),a n df(x+y) are in A.P. for all x , y ,a n df(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

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