CALCU-can you speak Chinese

can you speak Chinese

Yes, I can speak Chinese. 你好！你有什么问题吗？(Hello! Do you have any questions?)

你可以帮我对一个函数求导吗？

Solution by Steps

step 1

Identify the function to differentiate:

f(x) = \sum_{n=2}^{\infty} \left(\frac{\ln(n)}{3^n n^3}\right)x^n

step 2

Differentiate term by term:

f'(x) = \sum_{n=2}^{\infty} \left(\frac{\ln(n)}{3^n n^3}\right)nx^{n-1}

step 3

Simplify the derivative:

f'(x) = \sum_{n=2}^{\infty} \left(\frac{\ln(n)}{3^n n^2}\right)x^{n-1}

Answer

f'(x) = \sum_{n=2}^{\infty} \left(\frac{\ln(n)}{3^n n^2}\right)x^{n-1}

Key Concept

Power Series Differentiation

Explanation

The derivative of a power series can be found by differentiating each term individually, which involves bringing down the exponent as a coefficient and reducing the exponent by one.

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