d/dx(cosx)
To find the derivative of the function f(x) = cos(x) with respect to x (denoted as d/dx(cosx)), we can use the derivative rules for trigonometric functions
To find the derivative of the function f(x) = cos(x) with respect to x (denoted as d/dx(cosx)), we can use the derivative rules for trigonometric functions.
The derivative of the cosine function is equal to the negative sine function. Therefore, d/dx(cosx) = -sin(x).
To understand why this is the case, let’s break it down step by step:
1. Start with the function f(x) = cos(x).
2. We want to find the rate of change of f(x) with respect to x, which is the derivative d/dx(f(x)).
3. Using the derivative rules, we know that the derivative of the cosine function is equal to the derivative of the outer function times the derivative of the inner function. In this case, the outer function is f(x) = cos(x) and the inner function is x.
4. Derivative of the outer function: The derivative of cos(x) with respect to x is equal to -sin(x). This can be derived from the derivative formula of the sine function.
5. Derivative of the inner function: The derivative of x with respect to x is equal to 1.
6. Multiplying the derivatives of the outer and inner functions together gives us d/dx(cosx) = -sin(x).
Therefore, the derivative of cos(x) with respect to x is -sin(x).
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