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

asked Aug 16, 2023 153k views

1 vote

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

$Find the derivative of \sqrt({x^(2)*6^x})^9-example-1$

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3 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,

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

Khurram answered Aug 20, 2023

4.3k points

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