What is (2x^{2/3})'((4x)')^{-1/2} ?

The solution to (2x^{2/3})'((4x)')^{-1/2} is ((2x^{2/3})')/(((4x)')^{1/2)}

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simplify (2x^{2/3})'((4x)')^{-1/2}

simplify

(2 x^{\frac{2}{3}})^{'} ((4 x)^{'})^{- \frac{1}{2}}

\frac{( 2 x ^{\frac{2}{3}} ) '}{( ( 4 x ) ' ) ^{\frac{1}{2}}}

Solution steps

(2 x^{\frac{2}{3}})^{'} ((4 x)^{'})^{- \frac{1}{2}}

Apply exponent rule:

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

= \frac{1}{( ( 4 x ) ^{^{'}} ) ^{\frac{1}{2}}} (2 x^{\frac{2}{3}})^{^{'}}

Multiply fractions:

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

= \frac{1 ( 2 x ^{\frac{2}{3}} ) ^{^{'}}}{( ( 4 x ) ^{^{'}} ) ^{\frac{1}{2}}}

Multiply:

1 (2 x^{\frac{2}{3}})^{'} = (2 x^{\frac{2}{3}})^{'}

= \frac{( 2 x ^{\frac{2}{3}} ) ^{^{'}}}{( ( 4 x ) ^{^{'}} ) ^{\frac{1}{2}}}

\frac{( 8 ) ^{1}}{1 !} e^{- 8}

8 a^{2} (x - 2)^{2} ((x - 2)^{2} + 2 a - 3 a^{3} (x - 2))

(1.331 \cdot 1 0^{27}) \cdot 1 0^{- 0.4} (1.45 - 4.83)

What is (2x^{2/3})'((4x)')^{-1/2} ?
The solution to (2x^{2/3})'((4x)')^{-1/2} is ((2x^{2/3})')/(((4x)')^{1/2)}