Find Derivative(root3(6x^2))
This is the same as saying (6x^2)^3. We can take the derivative using the chain rule. With the chain rule, you multiply by the power, decrease the power by 1, and multiply by the derivative of the inside.3(6x^2)^212xor36x(6x^2)^2Hope this helps
\(\bf \sqrt[3]{6x^2}\implies (6x^2)^{\frac{1}{3}}\implies 6^{\frac{1}{3}}x^{\frac{2}{3}}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=6^{\frac{1}{3}}\cdot \cfrac{2}{3}x^{\frac{2}{3}-1}\implies 6^{\frac{1}{3}}\cdot \cfrac{2}{3}x^{-\frac{1}{3}}\implies 6^{\frac{1}{3}}\cdot \cfrac{2}{3}\cdot \cfrac{1}{x^{\frac{1}{3}}} \\\\\\\)\(\bf \cfrac{dy}{dx}=6^{\frac{1}{3}}\cdot \cfrac{2}{3x^{\frac{1}{3}}}\implies \cfrac{2\cdot 6^{\frac{1}{3}}}{3x^{\frac{1}{3}}}\implies \cfrac{2\sqrt[3]{6}}{3\sqrt[3]{x}}\implies \cfrac{2}{3}\sqrt[3]{\cfrac{6}{x}}\)
