d/dx(sinx)
cosx
To find the derivative of the function f(x) = sin(x), we can use the basic derivative rules. The derivative of sin(x) with respect to x is defined as the rate of change of sin(x) with respect to x, or the slope of the tangent line to the graph of sin(x) at any point.
To find the derivative, we can use the chain rule. Recall that the derivative of a composite function f(g(x)) is given by the derivative of the outer function multiplied by the derivative of the inner function.
In this case, the outer function is sin(x) and the inner function is x. The derivative of sin(x) is cos(x), and the derivative of x with respect to x is 1. Applying the chain rule, we have:
d/dx(sin(x)) = cos(x) * d/dx(x) = cos(x) * 1 = cos(x).
Therefore, the derivative of sin(x) with respect to x is cos(x).
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