d/dx(sinx)
To find the derivative of the function f(x) = sin(x), we use the derivative rules for trigonometric functions
To find the derivative of the function f(x) = sin(x), we use the derivative rules for trigonometric functions.
The derivative of sin(x) with respect to x (denoted as d/dx(sin(x))) is cos(x).
Explanation:
The derivative of a function measures the rate at which the function changes with respect to its independent variable, in this case, x.
For trigonometric functions, like sin(x), the derivative can be found using the chain rule. First, we need to recognize that sin(x) is a composition of two functions: the outer function sin(u) and the inner function u = x.
Using the chain rule, we differentiate the outer function sin(u) with respect to the inner function u, and then multiply it by the derivative of the inner function du/dx. In this case, the derivative of u with respect to x is simply 1, since u = x.
So, applying the chain rule, we have:
d/dx(sin(x)) = cos(u) * du/dx = cos(x) * 1 = cos(x)
Thus, the derivative of sin(x) with respect to x is cos(x).
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