Differentiating the Cosine Function

In this post, the derivative of the cosine function is found. To do this, the steps in reference 1 are followed. Start with a definition of a derivative, from this post: $\frac{df(x)}{dx}\bigg|_{a^+} \equiv \lim_{\Delta x \rightarrow 0^+} \frac{ f(a + \Delta x) – f(a) }{\Delta x} $. Since $f(x)$ and $\cos(x)$ are both functions of $x$, …

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Differentiating the Sine Function

From this post, one type of derivative is $\lim_{\Delta x\rightarrow0^+}\frac{f(a+\Delta x)-f(a)}{\Delta x}\equiv\frac{df(x)}{dx}\big|_{a^+}$ To be consistent with my previous interpretation of $0^+$ in this post, $\Delta x \rightarrow 0^+$ means constraining $\Delta x$ to positive numbers. Next, define $x$ and $a$ as variables for nonnegative real numbers, to avoid having a negative angle for the sine function. In this post, …

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