What do you mean, resp. do you have an example? If you mean ##\dfrac{d}{dx}\dfrac{d}{dx} y(x) = \dfrac{d^2 y(x)}{dx^2}## then it is simply the second derivative, the curvature. If you mean ##\dfrac{d}{dx} dy## then ##dy## is a linear function and ##\dfrac{d}{dx} dy = dy##.mertcan said:Hi, it may be interesting question but what is the
d (dy)/dx (y is function of x)? I think it is nearly zero but if it is 0 then how can we prove it?
I mean the second one but why the result is dy?fresh_42 said:What do you mean, resp. do you have an example? If you mean ##\dfrac{d}{dx}\dfrac{d}{dx} y(x) = \dfrac{d^2 y(x)}{dx^2}## then it is simply the second derivative, the curvature. If you mean ##\dfrac{d}{dx} dy## then ##dy## is a linear function and ##\dfrac{d}{dx} dy = dy##.
Because the tangent of a tangent is the tangent again.mertcan said:I mean the second one but why the result is dy?
mertcan said:I think it is nearly zero but if it is 0 then how can we prove it?
The derivative of infinitesimal value is a mathematical concept used to describe the instantaneous rate of change of a function at a specific point. It is the limit of the ratio of the change in the function's output to the change in its input, as the change in input approaches zero.
The derivative of infinitesimal value can be calculated using the limit definition, which involves finding the slope of a tangent line at a specific point on the function's graph. It can also be calculated using algebraic rules and formulas for different types of functions.
The derivative of infinitesimal value has many important applications in mathematics and science. It is used to solve optimization problems, model rates of change in physical systems, and analyze the behavior of functions and their graphs.
Yes, the derivative of infinitesimal value can be negative. This indicates that the function is decreasing at that point, and the slope of its tangent line is negative. Similarly, a positive derivative indicates that the function is increasing at that point.
The derivative of infinitesimal value is closely related to the concept of limits. In fact, the limit definition of the derivative is based on taking the limit as the change in input approaches zero. Additionally, the derivative is used to find the slope of the tangent line, which is the limit of the slopes of secant lines as they become closer and closer to the tangent line.