If f,g,a n dh are differentiable func...

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 ' ')'|`

Topper's Solved these Questions

INTEGRALS
BANSAL|Exercise All Questions|111 Videos
LOGARITHM
BANSAL|Exercise All Questions|110 Videos

Similar Questions

Explore conceptually related problems

Let f,g, h be differentiable functions of x. if Delta = |(f,g,h),((xf)',(xg)',(xh)'),((x^(2) f)'',(x^(2)g)'',(x^(2) h)'')|and, Delta' = |(f,g,h),(f',g',h'),((x^(n)f'')',(x^(n) g'')',(x^(n) h'')')| , then n =

If f(x) is a differentiable function of x then lim_(h rarr0)(f(x+3h)-f(x-2h))/(h)=

Let f be a twice differentiable function such that f''(x)=-f(x), and f'(x)=g(x),h(x)=[f(x)]^(2)+[g(x)]^(2) Find h(10) if h(5)=11

Let f and g be two differential functions such that f(x)=g'(1)sin x+(g''(2)-1)xg(x)=x^(2)-f'((pi)/(2))x+f''((-pi)/(2))

If f(x) is a twice differentiable function such that f'' (x) =-f,f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to

If f(x) and g(x) are non- periodic functions, then h(x)=f(g(x))is

Let f be a twice differentiable function such that f''(x)=-f(x)" and "f'(x)=g(x)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(a)=8" and "h(0)=2," then "h(2)=

If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

BANSAL-LIMITS AND DERIVATIVES-All Questions

if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...
Text Solution
|
If (1+x)^n=C0+C1+C2\ x^2+\ dot+Cn\ x^n , using derivatives prove th...
Text Solution
|
If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(x...
Text Solution
|
If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...
Text Solution
|
Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...
Text Solution
|
Evaluate ("Lim")(x->0)(xcosx-"ln"(1+x))/(x^2)
Text Solution
|
Evaluate find a and b if \ ("Lim")(x->0)(x(1+acosx)-bsinx)/(x^3)=1
Text Solution
|
("Lim")(x->0)(e^xsinx-x-x^2)/(x^2+x-"ln"(1-x))
Text Solution
|
Evaluate: ("Lim")(x->0)(1+sinx-cosx+"ln"(1-x))/(xtan^2x) -1/2 (b)...
Text Solution
|
Evaluate: ("Lim")(x->0)((log)(secx/2)(cosx))/((log)(secx)(cos(x//2))) ...
Text Solution
|
Evaluate: ("Lim")(x->1)(x^x-x)/(x-1-lnx)
Text Solution
|
Evaluate: ("Lim")(x->0)(1-cosx cos2x cos3x)/(x^2)
Text Solution
|
Evaluate: ("Lim")(x->0)((cosa x)^(1//m)-(cosb x)^(1//n))/(x^2)
Text Solution
|
Evaluate: ("Lim")(x->0^+)("c o s e c"x)^(1/(lnx))
Text Solution
|
Evaluate: ("Lim")(x->pi//2)(secx)^(cotx)
Text Solution
|
Evaluate: ("Lim")(x->0^+)(cotx)^(1/(lnx))
Text Solution
|
Evaluate: ("Lim")(x->0)(1/x)^(tanx)
Text Solution
|
Evaluate: ("Lim")(x->0)x^x
Text Solution
|
Evaluate: ("Lim")(x->1)(1-x^2)^(1/(ln(1-x)))
Text Solution
|
Evaluate: ("Lim")(x->4)(sqrt(2x+1)+sqrt(x-3)-4)/(sqrt((3x+4))+sqrt(5x+...
Text Solution
|