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

Popular >

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

\frac{1}{x x ^{2} - 1}

\frac{\partial}{\partial x} (7 cos (x) sin (y))

\frac{d}{d x} (\frac{e ^{3 x}}{x})

\frac{d}{d x} (ln (8 - 4 x))

\frac{d}{d x} (cos (x + e^{x}))

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