Khan academy business calculus10/29/2023 ![]() Derivative of a constant,Ĭhange with respect to x, so it's just equal to 0. ![]() Plus any constant, is going to be equal to 2x. So once again, this is justĭerivative, with respect to x of x squared ![]() Respect to x of 1, is just a constant, is just 0. Operator to x squared plus pi, I also get 2x. The derivative operator to x squared plusġ, I also get 2x. For instance, when integrating a variable x with respect to a measure μ, the notation dμ(x) is sometimes used to emphasize the dependence on x. Depending on the situation, the notation may vary slightly to capture the important features of the situation. If the underlying theory of integration is not important, dx can be seen as strictly a notation indicating that x is a dummy variable of integration if the integral is seen as a Riemann integral, dx indicates that the sum is over subintervals in the domain of x in a Riemann–Stieltjes integral, it indicates the weight applied to a subinterval in the sum in Lebesgue integration and its extensions, dx is a measure, a type of function which assigns sizes to sets in non-standard analysis, it is an infinitesimal and in the theory of differentiable manifolds, it is often a differential form, a quantity which assigns numbers to tangent vectors. In Leibniz's notation, dx is interpreted as an infinitesimal change in x and his integration notation is the most common one in use today. The symbol dx has different interpretations depending on the theory being used. ![]()
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