Natural log of a sum? (not sum of natural logs)

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SUMMARY

The discussion focuses on finding the derivative of the function y = x^2 + x^(2x). The correct approach involves using the linearity of the derivative operator, allowing the derivative to be computed as the sum of the derivatives of each term. Specifically, the derivative is calculated as dy/dx = d/dx(x^2) + d/dx(x^(2x)). This method effectively simplifies the differentiation process without the need for implicit differentiation or natural logarithms.

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yiyopr
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Homework Statement



Find the derivative of y = x^2 + x^(2x)

The Attempt at a Solution



By looking at the equation I think I need to use implicit differentiation + natural logs. But I can't do anything with:

lny = ln(x^2 + x^(2x))

So I assume I'm wrong.. Any help??
 
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yiyopr said:

Homework Statement



Find the derivative of y = x^2 + x^(2x)


The Attempt at a Solution



By looking at the equation I think I need to use implicit differentiation + natural logs. But I can't do anything with:

lny = ln(x^2 + x^(2x))

So I assume I'm wrong.. Any help??

Use the linearity of the derivative operator: \frac{dy}{dx} = \frac{d}{dx}\left(x^2+x^{2x} \right) = \frac{d}{dx}\left(x^2 \right) + \frac{d}{dx}\left(x^{2x} \right). Compute each derivative separately and then add the results.
 

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