What is (2/3 u^{-1/3}u')*3/2 u^{1/3} ?

The solution to (2/3 u^{-1/3}u')*3/2 u^{1/3} is u'

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simplify (2/3 u^{-1/3}u')*3/2 u^{1/3}

simplify

(\frac{2}{3} u^{- \frac{1}{3}} u^{'}) \cdot \frac{3}{2} u^{\frac{1}{3}}

u'

Solution steps

(\frac{2}{3} u^{- \frac{1}{3}} u^{'}) \frac{3}{2} u^{\frac{1}{3}}

Apply exponent rule:

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

= \frac{2}{3} \cdot \frac{3}{2} \cdot \frac{1}{u ^{\frac{1}{3}}} u^{\frac{1}{3}} u^{^{'}}

Multiply fractions:

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

= \frac{2 \cdot 1 \cdot 3 u ^{^{'}} u ^{\frac{1}{3}}}{3 u ^{\frac{1}{3}} \cdot 2}

Cancel the common factor:

2

= \frac{1 \cdot 3 u ^{^{'}} u ^{\frac{1}{3}}}{3 u ^{\frac{1}{3}}}

Cancel the common factor:

3

= \frac{1 u ^{^{'}} u ^{\frac{1}{3}}}{u ^{\frac{1}{3}}}

Cancel the common factor:

u^{\frac{1}{3}}

= 1 u^{^{'}}

Multiply:

1 u^{'} = u^{'}

= u^{^{'}}

e^{- \frac{l n ( 2 )}{l n ( 4 )}}

0.65 \cdot 1 0^{- 5}

(2 sin (x) cos (x))^{2}

20 \cdot 3785.41 \cdot 10 \cdot 1 \cdot 1 0^{- 3}

What is (2/3 u^{-1/3}u')*3/2 u^{1/3} ?
The solution to (2/3 u^{-1/3}u')*3/2 u^{1/3} is u'