Find the derivative using logarithmic differentiation method $\frac{\left(\sqrt[6]{\left(6a^2+b^2+11ab-10b^2\right)^{5}}\right)^2\left(3ab+2\right)^{-\frac{5}{3}}}{\left(4b-10\right)^{\frac{5}{3}}}$

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$\frac{d}{da}\left(\frac{\left(\sqrt[6]{\left(6a^2+b^2+11ab-10b^2\right)^{5}}\right)^2\left(3ab+2\right)^{-\frac{5}{3}}}{\sqrt[3]{\left(4b-10\right)^{5}}}\right)$

Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method ((6a^2+b^211ab-10b^2)^5/6^2(3ab+2)^(-5/3))/((4b-10)^(5/3)). Simplifying. Simplify the derivative by applying the properties of logarithms. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. To derive the function \frac{\sqrt{\left(3ab+2\right)^{5}}}, use the method of logarithmic differentiation. First, assign the function to y, then take the natural logarithm of both sides of the equation.