The value of `d/dx(x^x)`

The value of (d)/(dx)(|x-1|+|x-5|) at x=3, is

If f(x)=|x|+|x-1| , write the value of d/(dx)(f(x)) .

Write the value of d/(dx)(x \ |x|) .

Write the value of d/(dx){(x+|x|)|x|}dot

If f(x)=x+1 , then write the value of d/(dx)(fof)(x) .

Write the value of d/(dx)(log|x|) .

d/dx(x^n.logx)

If (d)/(dx)((1+x^2+x^4)/(1+x+x^2)) = a+bx , find the values of a and b .

If f(x)a n dg(x) a re differentiate functions, then show that f(x)+-g(x) are also differentiable such that d/(dx){f(x)+-g(x)}=d/(dx){f(x)}+-d/(dx){g(x)}

Using the first principle, prove that: d/(dx)(f(x)g(x))=f(x)d/(dx)(g(x))+g(x)d/(dx)(f(x))