Question

Find Derivative
(root3(6x^2))

Answer 1

`\bf \sqrt[3]{6x^2}\implies (6x^2)^{(1)/(3)}\implies 6^{(1)/(3)}x^{(2)/(3)}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=6^{(1)/(3)}\cdot \cfrac{2}{3}x^{(2)/(3)-1}\implies 6^{(1)/(3)}\cdot \cfrac{2}{3}x^{-(1)/(3)}\implies 6^{(1)/(3)}\cdot \cfrac{2}{3}\cdot \cfrac{1}{x^{(1)/(3)}} \\\\\\`


`\bf \cfrac{dy}{dx}=6^{(1)/(3)}\cdot \cfrac{2}{3x^{(1)/(3)}}\implies \cfrac{2\cdot 6^{(1)/(3)}}{3x^{(1)/(3)}}\implies \cfrac{2\sqrt[3]{6}}{3\sqrt[3]{x}}\implies \cfrac{2}{3}\sqrt[3]{\cfrac{6}{x}}`

Answer 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)^2*12x
or
36x*(6x^2)^2

Hope this helps