What is (d^3)/(d^3x)te^{-t} ?

The solution to (d^3)/(d^3x)te^{-t} is t/(e^tx)

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simplify (d^3)/(d^3x)te^{-t}

simplify

\frac{d ^{3}}{d ^{3} x} t e^{- t}

\frac{t}{e ^{t} x}

Solution steps

\frac{d ^{3}}{d ^{3} x} t e^{- t}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{d ^{3}}{d ^{3} x} \cdot \frac{1}{e ^{t}} t

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{d ^{3} \cdot 1 \cdot t}{d ^{3} x e ^{t}}

Cancel the common factor:

d^{3}

= \frac{1 \cdot t}{x e ^{t}}

Multiply:

1 \cdot t = t

= \frac{t}{e ^{t} x}

2 x - 3 \cdot x - 1

5.4 \cdot 1 0^{- 7}

5.4 \cdot 1 0^{- 6}

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

(4 r s^{3}) (6 r^{2} s^{3})