(u^(0)v^(-4)*(u^(-3)v^(3))^(-2))/(2u)

Simplify and Apply Exponent Rule: First, simplify the expression inside the parentheses and apply the exponent rule (a^m)^n = a^(m*n) to the term (u^(-3)v^(3))^(-2). (u^(0)v^(-4)*(u^(-3)v^(3))^(-2)) = u^(0)v^(-4)*u^(6)v^(-6)Combine Like Terms: Next, combine the like terms by adding the exponents of u and v. u^(0+6)v^(-4-6) = u^6v^(-10)Divide by 2u: Now, divide the simplified expression by 2u. (u^6v^(-10))/(2u) = (1/2) * u^(6-1) * v^(-10)Simplify by Subtracting Exponents: Simplify the expression by subtracting the exponents of u. (1/2) * u^5 * v^(-10)Write Negative Exponent as Reciprocal: Finally, write the negative exponent as a reciprocal to express the answer without negative exponents. (1/2) * u^5 * (1/v^10) = (u^5)/(2v^10)

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Find derivatives of using multiple formulae

Full solution

\frac{u^{0} v^{-4} \cdot\left(u^{-3} v^{3}\right)^{-2}}{2 u}

Simplify and Apply Exponent Rule: First, simplify the expression inside the parentheses and apply the exponent rule $(a^m)^n = a^{m*n}$ to the term $(u^{-3}v^{3})^{-2}$ . $\newline$ $(u^{0}v^{-4}*(u^{-3}v^{3})^{-2}) = u^{0}v^{-4}*u^{6}v^{-6}$
Combine Like Terms: Next, combine the like terms by adding the exponents of $u$ and $v$ . $\newline$ $u^{(0+6)}v^{(-4-6)} = u^6v^{(-10)}$
Divide by $2$ u: Now, divide the simplified expression by $2$ u. $\newline$ $(u^6v^{-10})/(2u) = (1/2) \times u^{(6-1)} \times v^{-10}$
Simplify by Subtracting Exponents: Simplify the expression by subtracting the exponents of $u$ . $\left(\frac{1}{2}\right) \cdot u^{5} \cdot v^{(-10)}$
Write Negative Exponent as Reciprocal: Finally, write the negative exponent as a reciprocal to express the answer without negative exponents. $\newline$ $(\frac{1}{2}) \times u^5 \times (\frac{1}{v^{10}}) = \frac{u^5}{2v^{10}}$