If f(x) and g(x) are differentiable for all, x then
`d/dx(f(g(x)))=f'(g(x)).g'(x)`

If both f(x) and g(x) are non-differentiable at x=a then f(x)+g(x) may be differentiable at x=a

Let f and g be differentiable functions such that: xg(f(x))f\'(g(x))g\'(x)=f(g(x))g\'(f(x))f\'(x) AA x in R Also, f(x)gt0 and g(x)gt0 AA x in R int_0^xf(g(t))dt=1-e^(-2x)/2, AA x in R and g(f(0))=1, h(x)=g(f(x))/f(g(x)) AA x in R Now answer the question: f(g(0))+g(f(0))= (A) 1 (B) 2 (C) 3 (D) 4

If x=f(t) and yy=g(t) are differentiable functions of t then (d^(2)y)/(dx^(2)) is

If f(x) and g(x) are two differentiable functions, show that f(x)g(x) is also differentiable such that (d)/(dx)[f(x)g(x)]=f(x)(d)/(dx){g(x)}+g(x)(d)/(dx){f(x)}

If f(x) and g(x) are differentiable function then show that f(x)+-g(x) are also differentiable such that d(f(x)+-g(x))/(dx)=d(f(x))/(dx)+-d(g(x))/(dx)

If f(x) and g(x) a re differentiate functions, then show that f(x)+-g(x) are also differentiable such that (d)/(dx){f(x)+-g(x)}=(d)/(dx){f(x)}+-(d)/(dx){g(x)}

If f(x) and g(f) are two differentiable functions and g(x)!=0, then show trht (f(x))/(g(x)) is also differentiable (d)/(dx){(f(x))/(g(x))}=(g(x)(d)/(pi){f(x)}-g(x)(d)/(x){g(x)})/([g(x)]^(2))

If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(xg)'(x h)'(x^(f2)f)' '(x^2g)' '(x^2h)' '| prove that ^(prime)=|fgff'g' h '(x^3f' ')'(x^3g' ')'(x^3h ' ')'|

Let f(x) and g(x) be two functions which are defined and differentiable for all x>=x_(0). If f(x_(0))=g(x_(0)) and f'(x)>g'(x) for all x>x_(0), then prove that f(x)>g(x) for all x>x_(0).

Iff (x) and g(x) be two function which are defined and differentiable for all x>=x_(0). If f(x_(0))=g(x_(0)) and f'(x)>g'(x) for all f>x_(0), then prove that f(x)>g(x) for all x>x_(0).