What is maclaurin 6e^{-5x} ?

The answer to maclaurin 6e^{-5x} is 6-30x+75x^2-125x^3+625/4 x^4+\ldots

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maclaurin 6e^{-5x}

maclaurin

6 e^{- 5 x}

6 - 30 x + 75 x^{2} - 125 x^{3} + \frac{625}{4} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 6 + \frac{\frac{d}{d x} ( 6 e ^{- 5 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 6 e ^{- 5 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 6 e ^{- 5 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 6 + \frac{- 30}{1 !} x + \frac{150}{2 !} x^{2} + \frac{- 750}{3 !} x^{3} + \frac{3750}{4 !} x^{4} + \dots

Refine

= 6 - 30 x + 75 x^{2} - 125 x^{3} + \frac{625}{4} x^{4} + \dots

(8 x)^{l n (8 x)}

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

x \to 0 lim (arcsin (x))

7 x^{4} arctan (2 x^{3})

y^{^{'}} = 2 x y + x

What is maclaurin 6e^{-5x} ?
The answer to maclaurin 6e^{-5x} is 6-30x+75x^2-125x^3+625/4 x^4+\ldots