The Chain Rule: Finding the Derivative of sin(x) and its Application in Mathematics

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. The chain rule states that if we have a composite function, f(g(x)), then the derivative can be found by taking the derivative of the outer function and multiplying it with the derivative of the inner function.

In this case, f(x) = sin(x) and g(x) = x. Therefore, we can write the composite function as f(g(x)) = sin(x).

To find the derivative, we will differentiate the sine function. The derivative of sin(x) is given by:

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

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

Therefore, d/dx(sin(x)) = cos(x).

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