using the first principle of differentiation, find the first derivatives of
- Thread starter Choi20
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Typically differentiating by first principles involves evaluating the limit:
\(\displaystyle \displaystyle f'(x)\equiv\lim_{h\to0}\frac{f(x+h)-f(x)}{h}\)
and then one seeks algebraically for a way to divide out the \(\displaystyle h\) in the denominator.
I'll set the limits up and leave you to to algebra, and please feel free to post your work if you get stuck.
1.) \(\displaystyle \displaystyle f'(x)=3\lim_{h\to0}\frac{\dfrac{1}{(x+h)^2}-\dfrac{1}{x^2}}{h}\)
2.) \(\displaystyle \displaystyle f'(x)=\lim_{h\to0}\frac{\dfrac{1}{(x+h)^{\frac{3}{2}}}-\dfrac{1}{x^{\frac{3}{2}}}}{h}\)
\(\displaystyle \displaystyle f'(x)\equiv\lim_{h\to0}\frac{f(x+h)-f(x)}{h}\)
and then one seeks algebraically for a way to divide out the \(\displaystyle h\) in the denominator.
I'll set the limits up and leave you to to algebra, and please feel free to post your work if you get stuck.
1.) \(\displaystyle \displaystyle f'(x)=3\lim_{h\to0}\frac{\dfrac{1}{(x+h)^2}-\dfrac{1}{x^2}}{h}\)
2.) \(\displaystyle \displaystyle f'(x)=\lim_{h\to0}\frac{\dfrac{1}{(x+h)^{\frac{3}{2}}}-\dfrac{1}{x^{\frac{3}{2}}}}{h}\)
D
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Well ... that would be the first thing you should learn.
Open the text-book and start working with the example problems....