d/dx(cosx)
To differentiate the function cos(x) with respect to x, we can use the rules of differentiation
To differentiate the function cos(x) with respect to x, we can use the rules of differentiation.
The derivative operator d/dx represents the rate of change of a function with respect to x. In this case, we want to find the derivative of the function cos(x).
The derivative of cos(x) can be found using the chain rule. The chain rule states that if we have a composite function, such as cos(x), we can find its derivative by multiplying the derivative of the outer function by the derivative of the inner function.
For the function cos(x), the outer function is cos(u), where u is the inner function of x. In this case, u = x.
To find d/dx(cosx), we can proceed as follows:
Step 1: Differentiate the outer function
The derivative of cos(u) with respect to u is -sin(u). Since u is equal to x in this case, the derivative of cos(x) with respect to x is -sin(x). This represents the rate of change of cos(x).
Step 2: Multiply by the derivative of the inner function
Since the inner function is x, its derivative with respect to x is 1.
Step 3: Combine the results
Multiplying -sin(x) by 1 gives us the final result:
d/dx(cosx) = -sin(x)
Therefore, the derivative of cos(x) with respect to x is -sin(x).
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