How to find the derivative of f(x) for a basic problem?

Thread starter jimit shah
Start date Sep 8, 2012
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SUMMARY

The discussion focuses on finding the derivative of the function f(x) = sin(x) - cos(x) within the interval 0 < x < 2π. The derivative of this function is f'(x) = cos(x) + sin(x). The conversation emphasizes that since there is only one independent variable, x, partial differentiation is not applicable in this scenario. The goal is to identify local extrema by analyzing the critical points derived from the first derivative.

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Understanding of basic calculus concepts, specifically derivatives.
Familiarity with trigonometric functions, particularly sine and cosine.
Knowledge of critical points and local extrema in calculus.
Ability to analyze functions over a specified interval.

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Study the application of the First Derivative Test for identifying local extrema.
Learn about the behavior of trigonometric functions over their periodic intervals.
Explore the concept of critical points and how to find them for various functions.
Investigate the use of graphing tools to visualize functions and their derivatives.

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Students studying calculus, educators teaching derivative concepts, and anyone interested in understanding local extrema of trigonometric functions.

Sep 8, 2012

jimit shah

find the valu of local extremum for f(x)=sin x-cos x,0<x<2∏.

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Sep 8, 2012

HallsofIvy

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Kind of a basic problem isn't it? Can you find the derivative of f(x)?

Looks like homework to me so I am going to move it.

I will also point out that, because there is only the single independent variable, x, there is NO "partial differentiation" here.