Simplifying the Chain Rule: Finding the Derivative of sin(x) with Respect to x

(d/dx) sin(x)

To find the derivative of sin(x) with respect to x, we can use the chain rule

To find the derivative of sin(x) with respect to x, we can use the chain rule. Let’s break it down step by step:

Step 1: Write down the original function:
f(x) = sin(x)

Step 2: Apply the chain rule:
(d/dx) f(g(x)) = f'(g(x)) * g'(x)

In this case, our g(x) is just x, so g'(x) is equal to 1.

Step 3: Find the derivative of f(x):
f'(x) = cos(x)

Step 4: Substitute f'(x) and g'(x) back into the chain rule:
(d/dx) sin(x) = cos(x) * 1

Step 5: Simplify the expression:
(d/dx) sin(x) = cos(x)

Therefore, the derivative of sin(x) with respect to x is cos(x).

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