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Mathematics 45 Online
OpenStudy (anonymous):

from the definition of the derivative of a function find f'(x) if y=f(x)=x^2+2

OpenStudy (anonymous):

The definition is: \[\lim_{ \lambda \rightarrow 0}\frac{f(x)-f(x+ \lambda)}{\lambda}\] So you would have: \[\lim_{\lambda \rightarrow 0}\frac{x^2+2-((x+\lambda)^2+2)}{\lambda}\] Foil it out and you should come to the conclusion (after taking the limit) that: f'(x)=2x

OpenStudy (anonymous):

so basically ((x+h)^2+2-(x^2+2))/h then simplify from there. thanks!

OpenStudy (anonymous):

Yup :D

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