What is expand-1/24 (-6e^{-6x}x-e^{-6x}) ?

The solution to expand-1/24 (-6e^{-6x}x-e^{-6x}) is (e^{-6x}x)/4+1/24 e^{-6x}

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expand-1/24 (-6e^{-6x}x-e^{-6x})

expand

- \frac{1}{24} (- 6 e^{- 6 x} x - e^{- 6 x})

\frac{e ^{- 6 x} x}{4} + \frac{1}{24} e^{- 6 x}

Solution steps

- \frac{1}{24} (- 6 e^{- 6 x} x - e^{- 6 x})

Apply the distributive law:

a (b - c) = ab - a c

a = - \frac{1}{24}, b = - 6 e^{- 6 x} x, c = e^{- 6 x}

= - \frac{1}{24} (- 6 e^{- 6 x} x) - (- \frac{1}{24}) e^{- 6 x}

Apply minus-plus rules

- (- a) = a

= 6 \cdot \frac{1}{24} e^{- 6 x} x + \frac{1}{24} e^{- 6 x}

Simplify

6 \cdot \frac{1}{24} e^{- 6 x} x + \frac{1}{24} e^{- 6 x} : \frac{e ^{- 6 x} x}{4} + \frac{1}{24} e^{- 6 x}

= \frac{e ^{- 6 x} x}{4} + \frac{1}{24} e^{- 6 x}

(9 cos (x) - 9 cos (9 x))^{2}

\frac{( 7 s ^{2} + 23 s + 30 )}{( s - 2 ) ( s ^{2} + 2 s + 5 )}

- 3 (1 + \frac{i}{n})^{2}

- 2 x (- 2 x^{3})

\frac{( x ^{2} + 14 x + 48 ) ( x + 6 )}{2}

What is expand-1/24 (-6e^{-6x}x-e^{-6x}) ?
The solution to expand-1/24 (-6e^{-6x}x-e^{-6x}) is (e^{-6x}x)/4+1/24 e^{-6x}