If f(x),g(x)a n dh(x) are three polyno...

If `f(x),g(x)a n dh(x)` are three polynomial of degree 2, then prove that `phi(x)=|f(x)g(x)h(x)f'(x)g'(x h '(x)f' '(x)g' '(x )h ' '(x)|` is:

Topper's Solved these Questions

BOARD PAPER SOLUTIONS
RESONANCE DPP ENGLISH|Exercise All Questions|65 Videos
DETERMINANTS
RESONANCE DPP ENGLISH|Exercise All Questions|4 Videos

Similar Questions

Explore conceptually related problems

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that "phi(x)=|{:(f(x),g(x),h(x)),(f'(x),g'(x),h'(x)),(f''(x),g''(x),h''(x)):}| is a constant polynomial.

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

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

If f(x) g(x) and h(x) are three polynomials of degree 2 and Delta = |( f(x), g(x), h(x)), (f'(x), g'(x), h'(x)), (f''(x), g''(x), h''(x))| then Delta(x) is a polynomial of degree (dashes denote the differentiation).

If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))| is a polynomial of degree (where f^n (x) represents nth derivative of f(x))

If g is inverse of f then prove that f''(g(x))=-g''(x)(f'(g(x)))^(3).

If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h 'f' 'g' ' h ' '| , then F^(prime)(x) is equal to 1 (b) 0 (c) -1 (d) f(x)dotg(x)doth(x)

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

RESONANCE DPP ENGLISH-CONTINUITY AND DIFFERENTIABILITY-All Questions

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(d...
Text Solution
|
Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...
Text Solution
|
If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove t...
Text Solution
|
Let f(x) be a polynomial.Then, the second order derivative of f(e^x) i...
Text Solution
|
about to only mathematics
Text Solution
|
If the function f(x)=(x^2)/2+lnx+a x is always monotonically increasi...
Text Solution
|
fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)}...
Text Solution
|
(d^2x)/(dy^2) equals: ((d^2y)/(dx^2))^(-1) (b) -((d^2y)/(dx^2))^(-1)(...
Text Solution
|
y=tan^(-1)""(4x)/(1+5x^(2))+tan^(-1)""(2+3x)/(3-2x)
Text Solution
|
If f (x) =lim (x to oo) x ((3)/(2) + [cos x)(sqrt(n^(2) +1)-sqrt(n ^(2...
Text Solution
|
If g(x)=(2h(x)+|h(x)|)/(2h(x)-|h(x)|) where h(x)=sinx-sin^n x ,n in R...
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
|
If If {:(" ""x"),(y=""),(" ""x"),(" ""a+")...
Text Solution
|
Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiatio...
Text Solution
|
If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)e ...
Text Solution
|
Let f(x)={s in2x ,0<xlt=pi//6a x+b ,pi//6<x<1 . If f(x)a n df^(prime)(...
Text Solution
|
If f is twice differentiable such that f''(x)=-f(x), f'(x)=g(x), h'(x...
Text Solution
|
Find (dy)/(dx) : x=a{cost+1/2logt a n^2t/2} and y=asint .
Text Solution
|
If x^m y^n=(x+y)^(m+n), prove that (dy)/(dx)=y/x .
Text Solution
|
If e^f(x)= log x and g(x) is the inverse function of f(x), then g'(x)...
Text Solution
|