The Derivative of Sin(x) Explained: Understanding the Rate of Change of the Sine Function

derivative sinx

To find the derivative of sin(x), we can use the basic rules of differentiation

To find the derivative of sin(x), we can use the basic rules of differentiation.

The derivative of a function represents the rate of change of that function at any given point. In the case of sin(x), the derivative will give us the rate at which the sine function is changing with respect to x.

The derivative of sin(x) can be found using the chain rule, which states that if we have a function f(g(x)), then the derivative of that function is given by the product of the derivative of f with respect to g and the derivative of g with respect to x.

In this case, f is sin(x), and g is x. So we need to find the derivative of sin(x) with respect to x.

The derivative of sin(x) is found by taking the derivative of the outer function (sin) and then multiplying it by the derivative of the inner function (x).

The derivative of sin(x) is given by:

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

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

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

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