Identify Function: We are asked to find the derivative of the function −cos(x)+5 with respect to x. The derivative of a function gives us the rate at which the function's value changes with respect to changes in the variable x. To find the derivative, we will use the basic differentiation rules for trigonometric functions and constants.
Differentiate Term by Term: The function we are differentiating is −cos(x)+5. We can differentiate this function term by term. The derivative of −cos(x) with respect to x is sin(x), because the derivative of cos(x) is −sin(x) and we have a negative sign in front of cos(x). The derivative of a constant, like 5, is 0.
Combine Results: Combining the results from the previous step, the derivative of −cos(x) is −(−sin(x)) which simplifies to sin(x), and the derivative of 5 is 0. So, the derivative of the entire function −cos(x)+5 is sin(x)+0.
Simplify Expression: Simplifying the expression from the previous step, we get that the derivative of −cos(x)+5 with respect to x is simply sin(x), since adding 0 does not change the value.
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