## d/dx(sin x) =

### To find the derivative of sin x with respect to x, we can use the basic differentiation rules

To find the derivative of sin x with respect to x, we can use the basic differentiation rules.

The derivative of a function represents its rate of change with respect to the independent variable. In this case, we are finding the rate of change of sin x with respect to x.

To differentiate sin x, we will use the chain rule. According to the chain rule, if we have a composite function f(g(x)), the derivative is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, the outer function is sin u, and the inner function is x.

The derivative of sin u with respect to u is cos u. (This is a fundamental derivative since the derivative of sin x is cos x).

Therefore, by the chain rule, the derivative of sin x with respect to x is cos x.

In mathematical notation:

d/dx(sin x) = cos x

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