Mathematics, 23.08.2019 20:40 Battboi
How do i derive (x^-4) using the limit definition [f(x+h) - f(x) / h]
Answers: 1
![f'(x)=\lim\limits_{h\to0}\frac{f(x-h)-f(x)}{h}\\\\f(x)=x^{-4}=\frac{1}{x^4}\\\\f'(x)=\lim\limits_{h\to0}\frac{(x+h)^{-4}-x^{-4}}{h}=\lim\limits_{h\to0}\frac{\frac{1}{(x+h)^4}-\frac{1}{x^4}}{h}=\lim\limits_{h\to0}\frac{\frac{x^4-(x+h)^4}{x^4(x+h)^4}}{h}\\\\=\lim\limits_{h\to0}\left[\frac{x^4-x^4-4x^3h-6x^2h^2-4xh^3-h^4}{x^4(x+h)^4}\cdot\frac{1}{h}\right]=\lim\limits_{h\to0}\frac{-4x^3h-6x^2h^2-4xh^3-h^4}{hx^4(x+h)^4}](/tpl/images/0191/8866/6fee6.png)
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How do i derive (x^-4) using the limit definition [f(x+h) - f(x) / h]...
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