Find an anti-derivative of the function `f(x)\ g"(x)-` `f"(x)\ g(x)`

Find an anti-derivative of the function f(x)=1/x

Sajan finds the derivate of two functions f(x) = x^2 + cos x and g(x) = x^2 cos x as follows f(x) = x^2 + cos x , f'(x) = 2x - sin x, g (x) = x^2 cos x , g'(x) = 2x ( - sin x) Sajan makes a mistake in finding derivative of one of the functions. Identify that function and find out correct derivate of that function

Find the derivative of f (x) w.r.t. g(x) for the f (x) = log x, g (x) = a ^(x)

Find the derivative of f (x) w.r.t. g(x) for the f (x) = e ^(x), g (x) = sqrtx)

If f and g are two functions having derivative of order three for all x satisfying f(x)g(x)=C (constant) and (f''')/(f')-"A" (f'')/f -(g''')/(g')+(3g")/g=0 . Then A is equal to

If f and g are two functions having derivative of order three for all x satisfying f(x)g(x)=C (constant) and (f''')/(f')-"A" (f'')/f -(g''')/(g')+(3g")/g=0 . Then A is equal to

let f(x)=sqrt(x) and g(x)=x be function defined over the set of non negative real numbers. find (f+g)(x),(f-g)(x),(fg)(x) and (f/g)(x)

If f and g are derivable function of x such that g'(a)ne0,g(a)=b" and "f(g(x))=x," then 'f'(b)=

Suppose f and g are functions having second derivatives f'' and g'' every where . If f(x) .g(x) = 1 for all x and f' and g' are never zero then (f''(x))/(f'(x))-(g''(x))/(g'(x)) equals