What is 50*10^{-3}*derivative of 2xe^{-4x} ?

The solution to 50*10^{-3}*derivative of 2xe^{-4x} is (derivative of 2e^{-4x}x)/(20)

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simplify 5010^{-3}derivative of 2xe^{-4x}

simplify

50 \cdot 1 0^{- 3} \cdot \frac{d}{d x} (2 x e^{- 4 x})

\frac{\frac{d}{d x} ( 2 e ^{- 4 x} x )}{20}

Solution steps

50 \cdot 1 0^{- 3} \frac{d}{d x} (2 x e^{- 4 x})

Apply exponent rule:

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

= 50 \cdot \frac{1}{1 0 ^{3}} \frac{d}{d x} (2 e^{- 4 x} x)

Multiply fractions:

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

= \frac{1 \cdot 50 \frac{d}{d x} ( 2 x e ^{- 4 x} )}{1 0 ^{3}}

Multiply the numbers:

1 \cdot 50 = 50

= \frac{50 \frac{d}{d x} ( 2 e ^{- 4 x} x )}{1 0 ^{3}}

Factor

50 : 5^{2} \cdot 2

Factor

1 0^{3} : 2^{3} \cdot 5^{3}

= \frac{5 ^{2} \cdot 2 \frac{d}{d x} ( 2 e ^{- 4 x} x )}{2 ^{3} \cdot 5 ^{3}}

Cancel

\frac{2 \cdot 5 ^{2} \frac{d}{d x} ( 2 x e ^{- 4 x} )}{2 ^{3} \cdot 5 ^{3}} : \frac{\frac{d}{d x} ( 2 x e ^{- 4 x} )}{2 ^{2} \cdot 5}

= \frac{\frac{d}{d x} ( 2 x e ^{- 4 x} )}{2 ^{2} \cdot 5}

2^{2} \cdot 5 = 20

= \frac{\frac{d}{d x} ( 2 x e ^{- 4 x} )}{20}

200 \cdot 729. 7^{- 8}

\frac{( 60 ) ^{2}}{( 0.02 ) ^{2}}

e^{- 7 t} cosh (2 t)

e^{- (0.5)}

- 16 e^{2 t} sin (2 t) \cdot e^{- 2 t} (2 sin (2 t))

What is 50*10^{-3}*derivative of 2xe^{-4x} ?
The solution to 50*10^{-3}*derivative of 2xe^{-4x} is (derivative of 2e^{-4x}x)/(20)