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

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`

Text Solution

AI Generated Solution

Topper's Solved these Questions

DIFFERENTIALS, ERRORS AND APPROXIMATIONS
RD SHARMA ENGLISH|Exercise All Questions|107 Videos
DIRECTION COSINES AND DIRECTION RATIOS
RD SHARMA ENGLISH|Exercise All Questions|90 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:

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)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) 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))

int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x))/(f(x)*g(x)){logg(x)-logf(x)} \ dx

If y=|f(x)g(x)h(x)l m n a b c| , prove that (dy)/(dx)=|f^(prime)(x)g^(prime)(x)h^(prime)(x)l m n a b c| .

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions

If f(x)=|[x+a^2 , a b , a c],[a b, x+b^2,b c],[ ac,b c, x+c^2]|. then ...
Text Solution
|
If fr(x),gr(x),hr(x),r=1,2,3 are polynomials such that fr(a)=gr(a)=hr...
Text Solution
|
If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...
Text Solution
|
If f,g, and h are differentiable functions of x and "delta"=|[f,g,h...
Text Solution
|
If y=|f(x)g(x)h(x)l m n a b c| , prove that (dy)/(dx)=|f^(prime)(x)g^(...
Text Solution
|
If f(x)=(log)e((log)e x) , then write the value of f^(prime)(e) .
Text Solution
|
If f(x)=x+1 , then write the value of d/(dx)(fof)(x) .
Text Solution
|
If f^(prime)(1)=2 and y=f((log)e x) , find (dy)/(dx) at x=e .
Text Solution
|
If f(1)=4 , f^(prime)(1)=2 , find the value of the derivative of lo...
Text Solution
|
If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2) , then find (dy)/(dx) at x=1...
Text Solution
|
Let g(x) be the inverse of an invertible function f(x) which is deri...
Text Solution
|
If y=sin^(-1)(sinx) , -pi/2lt=xlt=pi/2 . Then, write the value of (...
Text Solution
|
Find dy/dx if x=sin2y
Text Solution
|
If pilt=xlt=2pi and y=cos^(-1)(cosx) , find (dy)/(dx) .
Text Solution
|
Find dy/dx if x=sin^2y
Text Solution
|
If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , wr...
Text Solution
|
If y=x|x| , find (dy)/(dx) for x<0 .
Text Solution
|
If y=sin^(-1)x+cos^(-1)x ,\ find (dy)/(dx) .
Text Solution
|
If x=a(theta+sintheta),\ \ y=a(1+costheta) , find (dy)/(dx) .
Text Solution
|
If y=x^x , find (dy)/(dx) at x=e .
Text Solution
|