What is taylor x^{x^2},1 ?

The answer to taylor x^{x^2},1 is 1+(x-1)+2(x-1)^2+2(x-1)^3+13/6 (x-1)^4+\ldots

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taylor x^{x^2},1

taylor

x^{x^{2}}, 1

1 + (x - 1) + 2 (x - 1)^{2} + 2 (x - 1)^{3} + \frac{13}{6} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( x ^{x^{2}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{x^{2}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{x^{2}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{1}{1 !} (x - 1) + \frac{4}{2 !} (x - 1)^{2} + \frac{12}{3 !} (x - 1)^{3} + \frac{52}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + (x - 1) + 2 (x - 1)^{2} + 2 (x - 1)^{3} + \frac{13}{6} (x - 1)^{4} + \dots

What is taylor x^{x^2},1 ?
The answer to taylor x^{x^2},1 is 1+(x-1)+2(x-1)^2+2(x-1)^3+13/6 (x-1)^4+\ldots