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(d)/(dx)(x^(x))=...

(d)/(dx)(x^(x))=

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The differentiation of e^(x) with respect to x is e^(x). i.e.(d)/(dx)(e^(x))=e^(x)

(d)/(dx)(a^(x)),a>0=

(d)/(dx)((x^(2))/(x-1))=

(d)/(dx)|x|

(d)/(dx)(x^((1)/(x)))

(d)/(dx)(a^(x)+x^(a))=?

(d)/(dx)(x^((1)/(3)))=

(d)/(dx)sin(x^(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))

If (d)/(dx)[f(x)]=(1)/(1+x^(2))," then: "(d)/(dx)[f(x^(3))]=