Find the derivative of \sqrt({x^(2)*6^x})^9

Question

Find the derivative of
`\sqrt({x^(2)*6^x})^9`

Answer 1

Answer:
`9x^8 6^(9x/2)+\ln(6^(4.5)) \cdot 6^(4.5x)`

Explanation:

`w=√((x^2 6^x)^9)=(x^2 6^x)^(9/2)=x^9 6^(9x/2)\\\\`

Using the product rule,

`(dw)/(dx)=6^(9x/2)(d)/(dx) (x^9)+x^9 (d)/(dx)(6^(9x/2))\\\\=9x^8 6^(9x/2)+\ln(6^(4.5)) \cdot 6^(4.5x)`