Understanding the Chain Rule | Finding the Derivative of the Sine Function

d/dx(sin(x))

To find the derivative of a function with respect to x, we use the rules of differentiation

To find the derivative of a function with respect to x, we use the rules of differentiation. Let’s find the derivative of the sine function, sin(x).

The derivative of sin(x) can be computed using the chain rule. The chain rule states that if we have a composite function, such as sin(x), we need to differentiate the outer function (in this case, sin) and multiply it by the derivative of the inner function (x).

The derivative of sin(x) can be written as d/dx(sin(x)) or simply sin'(x).

Using the chain rule, we start by differentiating the outer function:
The derivative of sin(x) is cos(x).

Now we multiply it by the derivative of the inner function, which is 1:
sin'(x) = cos(x) * 1 = cos(x).

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

In summary:
d/dx(sin(x)) = cos(x).

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