Let g(x) be the inverse of an invertible...

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real x. Then g''(f(x)) equals

`-(f''(x))/((f'(x))^(3))`

`(f'(x)f''(x)-(f(x))^(3))/(f'(x))`

`(f'(x)f''(x)-(f'(x))^(2))/((f'(x))^(2))`

none of these

Text Solution

Verified by Experts

`"Given that "g^(-1)(x)=f(x)`
`"or "x=g(f(x))`
`"or "g'(f(x))f'(x)=1`
`"or "g'(f(x))=(1)/(f'(x))`
`"or "g''(f(x))f'(x)=(-f''(x))/([f'(x)]^(2))`
`"or "g''(f(x))=(-f''(x))/([f'(x)]^(3))`

Topper's Solved these Questions

DIFFERENTIATION
CENGAGE|Exercise Exercise (Multiple)|22 Videos
DIFFERENTIATION
CENGAGE|Exercise Exercise (Comprehension)|23 Videos
DIFFERENTIATION
CENGAGE|Exercise Exercise 3.9|14 Videos
DIFFERENTIAL EQUATIONS
CENGAGE|Exercise Question Bank|25 Videos
DOT PRODUCT
CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

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

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all x, then g'f(x) is equal to

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g'(f(x)) equal.(a) f'(c)( b) (1)/(f'(c)) (c) f(c) (d) none of these

Let g(x) be the inverse of an invertible function f(x) which is derivable at x=3. If f(3)=9 and f'(3)=9, write the value of g'(9).

A function f(x) is differentiable at x=c(c in R). Let g(x)=|f(x)|,f(c)=0 then

Let g(x) be the inverse of the function f(x) ,and f'(x) 1/(1+ x^(3)) then g(x) equals

Let g(x) be the inverse of the function f(x) and f'(x)=(1)/(1+x^(3)) then g'(x) equals

Let g(x) be the inverse of the function f(x)=ln x^(2),x>0 . If a,b,c in R ,then g(a+b+c) is equal to

Let f(x) be differentiable function and g(x) be twice differentiable function.Zeros of f(x),g'(x) be a,b, respectively,(a

CENGAGE-DIFFERENTIATION-Exercise (Single)

If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...
Text Solution
|
"If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...
Text Solution
|
If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is
Text Solution
|
A function f satisfies the condition f(x)=f'(x)+f''(x)+f''(x)+…, where...
Text Solution
|
Let f(x) be a polynomial of degree 3 such that f(3)=1, f'(3)=-1, f''(3...
Text Solution
|
If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...
Text Solution
|
"If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=
Text Solution
|
If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...
Text Solution
|
Let y=in (1+ cos x)^(2). The the value of (d^(2)y)/(dx^(2))+(2)/(e^(y/...
Text Solution
|
x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)a tt=pi/2 is (pi+4)/2 (b) -(p...
Text Solution
|
"Let "y=t^(10)+1 and x=t^(8)+1." Then "(d^(2)y)/(dx^(2)) is
Text Solution
|
If x = log p and y=(1)/(p), then
Text Solution
|
If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^...
Text Solution
|
If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) ...
Text Solution
|
Let g(x) be the inverse of an invertible function f(x), which is diffe...
Text Solution
|
f(x)=e^(x)-e^(-x)-2 sin x -(2)/(3)x^(3). Then the least value of n for...
Text Solution
|
Let y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda(z^(3))(dy)/(dz)...
Text Solution
|
Let x=f(t) and y=g(t), where x and y are twice differentiable function...
Text Solution
|
If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in ...
Text Solution
|
A function f: R rarr R" satisfies sin x cos y "(f(2x+2y)-f(2x-2y))= co...
Text Solution
|