Question

9.) Note that in class we learned that the derivative of cos x is equal to sin x. Notice that these are both periodic functions. Argue if the derivative of a differentiable periodic function will always be periodic. Note: I'm going to make this on the quality of your argument, not on if it's correct or not. [2T]

          9.)
Note that in class we learned that the derivative of cos x is equal to sin x. Notice that these are both periodic
functions. Argue if the derivative of a differentiable periodic function will always be periodic. Note: I'm going to make
this on the quality of your argument, not on if it's correct or not. [2T]

9.)
Note that in class we learned that the derivative of cos x is equal to sin x. Notice that these are both periodic
functions. Argue if the derivative of a differentiable periodic function will always be periodic. Note: I'm going to make
this on the quality of your argument, not on if it's correct or not. [2T]

Added by Nerea S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Imogen Dell

Step 1

This means that for any x, we have f(x+T) = f(x). Now, let's take the derivative of f(x) with respect to x. By the definition of the derivative, we have: f'(x) = lim(h->0) [f(x+h) - f(x)] / h Since f(x) is periodic, we can substitute x+h with x+T, since adding Show more…

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Note that in class, we learned that the derivative of cos x is equal to sin x. Notice that these are both periodic functions. Argue if the derivative of a differentiable periodic function will always be periodic. Note: I'm going to base this on the quality of your argument, not on if it's correct or not. [2T]