What is maclaurin e^{((x^5))/5} ?

The answer to maclaurin e^{((x^5))/5} is 1+1/5 x^5+1/50 x^{10}+\ldots

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maclaurin e^{((x^5))/5}

maclaurin

e^{\frac{( x ^{5} )}{5}}

1 + \frac{1}{5} x^{5} + \frac{1}{50} x^{10} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{\frac{x ^{5}}{5}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{\frac{x ^{5}}{5}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{\frac{x ^{5}}{5}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{24}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{72576}{10 !} x^{10} + \dots

Refine

= 1 + \frac{1}{5} x^{5} + \frac{1}{50} x^{10} + \dots

\frac{1}{( 1 - t ^{2} ) ^{\frac{1}{2}}}

f (x) = (\frac{x + 1}{x + 3})^{2}, at x = - 2

\int_{0}^{\infty} \frac{( y e ^{- \frac{y}{a}} )}{a} d y

y = x^{2} - 4 x, y = 2 x + 7

\frac{d y}{d x} = \frac{x ^{3} - y ^{3}}{3 x y ^{2}}

What is maclaurin e^{((x^5))/5} ?
The answer to maclaurin e^{((x^5))/5} is 1+1/5 x^5+1/50 x^{10}+\ldots