What is maclaurin f(x)=e^x ?

The answer to maclaurin f(x)=e^x is sum from n=0 to infinity of (x^n)/(n!)

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maclaurin f(x)=e^x

maclaurin

f (x) = e^{x}

n = 0 \sum \infty \frac{x ^{n}}{n !}

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{1}{2 !} x^{2} + \frac{1}{3 !} x^{3} + \frac{1}{4 !} x^{4} + \dots

The series sum representation

= n = 0 \sum \infty \frac{x ^{n}}{n !}

\frac{d}{d x} (sin^{1} (x))

\frac{e ^{- 4 s}}{( 5 s ^{2} + 20 )}

\int (\frac{7}{t ^{2}} - 5 t^{5}) d t

\frac{\partial}{\partial x} (e^{x} + e^{y})

\int (\frac{3}{x ^{4}}) d x

What is maclaurin f(x)=e^x ?
The answer to maclaurin f(x)=e^x is sum from n=0 to infinity of (x^n)/(n!)