Question and Answers Forum

All Questions      Topic List

Differentiation Questions

Previous in All Question      Next in All Question      

Previous in Differentiation      Next in Differentiation      

Question Number 22105 by j.masanja06@gmail.com last updated on 11/Oct/17

$$usethefirstprincipletofind$$$$valueof$$$$f\left(x\right)={\left(x\right)}^{\frac{1}{3}}$$

Answered by $@ty@m last updated on 11/Oct/17

$$\frac{dy}{dx}=\underset{\delta x\to 0}{\lim }\frac{f(x+\delta x)-f\left(x\right)}{\delta x}$$$$=\underset{x+\delta x\to x}{\lim }\frac{{(x+\delta x)}^{\frac{1}{3}}-x^{\frac{1}{3}}}{(x+\delta x)-x}$$$$=\frac{1}{3}{x}^{\frac{1}{3}-1},usingformula\underset{x\to a}{\lim }\frac{x^n-a^n}{x-a}={na}^{n-1}$$$$=\frac{1}{3x^{\frac{2}{3}}}Ans.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com