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,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 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))

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 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)=

Let f be twice differentiable function such that g'(x)=-(f(x))/(g(x)),f'(x)=(g(x))/(f(x))h(x)=e^((f(x))^(2)+(g(x))^(2)+x)If h(5)=e^(6) then h(10) is equal to

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_r(x),g_r(x),h_r(x),r=1,2,3 are differentiable function and y=|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))| then dy/dx= |(f\'_1(x), g\'_1(x), h\'_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))|+ |(f_1(x), g_1(x), h_1(x)), (f\'_2(x), g\'_2(x), h\'_2(x)),(f_3(x), g_3(x), h_3(x))|+|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f\'_3(x), g\'_3(x), h\'_3(x))| On the basis of above information, answer the following question: Let f(x)=|(x^4, cosx, sinx),(24, 0, 1),(a, a^2, a^3)| , where a is a constant Then at x= pi/2, d^4/dx^4{f(x)} is (A) 0 (B) a (C) a+a^3 (D) a+a^4