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Let there be $$f(x)=\frac{x^2+2^x}{x^2\cdot 2^x}$$ I'm asked to calculate $f'(1)$. I know that I should apply the division rule, then find the derivative $f'(x)$ while applying power, chain and product rules when necessary, and finally evaluate $f'(1)$.

The thing is all these steps seemed way to lengthy to me. I figured out that maybe there somehow was a shorter way to find $f'(x)$ without going through all these lengthy calculations.

Any help would be appreciated and thanks in advance.

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Note that $$f(x)=\frac{x^2+2^x}{x^2\cdot 2^x}=2^{-x}+x^{-2}.$$

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