1. The problem is to differentiate common trigonometric functions such as $\sin x$, $\cos x$, $\tan x$, etc. 2. Recall the basic derivatives: - The derivative of $\sin x$ is $\cos x$. - The derivative of $\cos x$ is $-\sin x$. - The derivative of $\tan x$ is $\sec^2 x$. 3. Let's differentiate each function step-by-step. **Example 1:** Differentiate $f(x) = \sin x$. Step 1: Write the function: $f(x) = \sin x$. Step 2: Use the derivative rule: $\frac{d}{dx}\sin x = \cos x$. Step 3: So, $f'(x) = \cos x$. **Example 2:** Differentiate $g(x) = \cos x$. Step 1: Write the function: $g(x) = \cos x$. Step 2: Use the derivative rule: $\frac{d}{dx}\cos x = -\sin x$. Step 3: So, $g'(x) = -\sin x$. **Example 3:** Differentiate $h(x) = \tan x$. Step 1: Write the function: $h(x) = \tan x$. Step 2: Use the derivative rule: $\frac{d}{dx}\tan x = \sec^2 x$. Step 3: So, $h'(x) = \sec^2 x$. These are the fundamental derivatives for trig functions which can be applied and combined with chain rule for more complex expressions.