Why is the differentiation of sinx cosx

Telekolleg - mathematics


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How does the differentiation of a sum of functions work? You can find out here.

Status: 04/22/2013 | archive

The differentiation of a sum of functions is shown using two examples:

Differentiating a sum of functions

s (x) = x2 + x5 =>
s' (x) = 2x + 5x4 s (x) =
2 sin x = sin x + sin x =>
s' (x) = 2 · cos x = cos x + cos x

Making the hypothesis

Making the hypothesis

Now, as a continuation of the above procedure, the hypothesis is set up: s (x) = x + sin x => s' (x) = 1 + cos x

Graphic representation

Graphical representation of s (x) = x + sin x

First, the graph of the function s (x) = x + sin x is displayed on the computer, showing a sine line running diagonally upwards.

Course of the input and output voltage of the C-R element

An experiment with the function generator, which this time generates a voltage U (t) = U t + U sin ωt, shows at the input the rising sine line known from the computer and at the output actually a cosine line shifted up by the summand 1, i.e. the Hypothesis has been confirmed experimentally. Even if the time increase for the input voltage is changed, the summand for the cosine voltage at the output changes proportionally.