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Lösung 1.1:2f

Aus Online Mathematik Brückenkurs 2

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We can rewrite the function using a trigonometric addition formula:


fx=cosx+3=cosxcos3−sinxsin3 


If we now differentiate this expression, cos3 and sin3 are constants and we obtain


fx=ddxcosxcos3−sinxsin3=cos3ddxcosx−sin3ddxsinx=cos3−sinx−sin3cosx


If we then use the addition formula in reverse, this gives


fx=−sinxcos3+cosxsin3=−sinx+3 

NOTE: In the next section, we will go through differentiation rules which make it possible to differentiate the expression directly without rewriting in this way.

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.1:2f“