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Is there any other anti derivative of 1 divided by x?
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
Why does an answer to an integration problem involve a Constant of Integration?
The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
What is the purpose of differential calculus?
Differential Calculus is to take the derivative of the function. It is important as it can be applied and supports other branches of science. For ex, If you have a velocity function, you can get its acceleration function by taking its derivative, same relationship as well with area and volume formulas.
When finding the derivative of a point on a piecewise function does every function in the piecewise function need to be continuous and approach the same limit?
All differentiable functions need be continuous at least.
What is the integral of the derivative with respect to x of a function of x divided by that same function of x with respect to x?
∫ f'(x)/f(x) dx = ln(f(x)) + C C is the constant of integration.
Why its said that derivation is reverse of antiderivatives?
It is said that derivation is reverse of antiderivation because that is the terminology.If you have a function f(x), then the derivative d/dx f(x) is the slope of the function f(x) at each x. This derivative could be called g(x). Sometimes it is called f'(x), but lets call it g(x).Now, start over...If you have a function g(x), then the antiderivative is a function f(x) such that the derivative d/dx f(x) is g(x). This may sound like circular definition, but it is not...If the derivative of f(x) is g(x), then the antiderivative of g(x) is f(x). Technically, the antiderivative of g(x) is f(x) + C, where C is any constant. This is true because the derivative of a constant C is zero.Now - terminology.Taking the derivative is the same thing as derivation.Taking the antiderivative is the same thing as reverse derivation.Taking the deriviative is the same thing as reverse antiderivation.Antiderivation is also called integration and that is the next topic after derivation. They are simply the reverse processes of each other.
Is there any other anti derivative of 1 divided by x?
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
How do you get the second derivative of potential energy?
To get the second derivative of potential energy, you first need to calculate the first derivative of potential energy with respect to the variable of interest. Then, you calculate the derivative of this expression. This second derivative gives you the rate of change of the slope of the potential energy curve, providing insight into the curvature of the potential energy surface.
Why does an answer to an integration problem involve a Constant of Integration?
The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
What is the purpose of differential calculus?
Differential Calculus is to take the derivative of the function. It is important as it can be applied and supports other branches of science. For ex, If you have a velocity function, you can get its acceleration function by taking its derivative, same relationship as well with area and volume formulas.
When finding the derivative of a point on a piecewise function does every function in the piecewise function need to be continuous and approach the same limit?
All differentiable functions need be continuous at least.
What is differentiate in mathematics?
Calculus! So, when you differentiate a function or find the derivative, as it is also called, you are finding the rate of change of the function. An easy way to find the derivative at a certain point on a function is to draw a line tangent to the function at that point; the slope of the tangent line is the derivative.
Does Derivative classification does have the same impact and effects as original classification?
does Derivative classification have the same impact and effects as original classification
What is the integral of the derivative with respect to x of a function of x divided by that same function of x with respect to x?
∫ f'(x)/f(x) dx = ln(f(x)) + C C is the constant of integration.
What are derivates?
The spacial derivative is the measure of a quantity as and how it is being changed in space. This is different from a temporal derivative and partial derivative.
What do you call a function whose graph is a non-vertical line?
It is a function. If the graph contains at least two points on the same vertical line, then it is not a function. This is called the vertical line test.
What is the derivative of tan x?
The derivative of tan(x) is sec2(x).(Which is the same as 1/cos2(x).
