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

Find the derivative of \sqrt({x^(2)*6^x})^9-example-1
User JeeBee
by
2.8k points

1 Answer

9 votes
9 votes

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)

User Surajit Biswas
by
3.1k points
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