A Comprehensive Guide to Finding the Derivative of the Function f(x) = sin(x) Using Trigonometric Rules

d/dx[sinx]

To find the derivative of the function f(x) = sin(x) with respect to x, you can use the knowledge of the derivatives of trigonometric functions

To find the derivative of the function f(x) = sin(x) with respect to x, you can use the knowledge of the derivatives of trigonometric functions.

The derivative of the sin function, denoted as d/dx[sin(x)] or f'(x), is equal to the cosine function. Therefore, the derivative of sin(x) is cos(x).

Mathematically, we can express this as:

d/dx[sin(x)] = cos(x)

Now, let’s go through the steps to understand why this is true:

Step 1: Start with the function f(x) = sin(x).

Step 2: Use the definition of the derivative to find the rate of change of f(x) with respect to x. This is denoted as d/dx[sin(x)] or f'(x).

Step 3: Apply the derivative rules for trigonometric functions. The derivative of sin(x) is equal to the cosine function, cos(x).

Therefore, the derivative of sin(x) is cos(x):

d/dx[sin(x)] = cos(x)

So, if you want to find the derivative of sin(x) at a specific point, you can substitute that value into the derivative formula and evaluate it.

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