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What is the integral of the derivative with respect to x of a function of x multiplied by another function of x with respect to x?
Mrkbh
∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g/(x) dx
This is known as integration by parts.
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∙ 13y ago
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What is the difference between differential and derivative in the field of calculus?
The derivative refers to the rate at which a function changes with respect to another measure. The differential refers to the actual change in a function across a parameter. The differential of a function is equal to its derivative multiplied by the differential of the independent variable . The derivative of a function is the the LIMIT of the ratio of the increment of a function to the increment of the independent variable as the latter tends to zero.
How do you get the second derivative of potential energy?
The same way you get the second derivative from any function. Assuming you have a function that expresses potential energy as a function of time, or perhaps as a function of position, you take the derivate of this function. This will give you another function. Then, you take the derivate of this derivative, to get the second derivative.
What is the derivative of just a constant?
0 A derivative is the rate of change of a function as another variable changes. As there is no change to a constant, the derivative is necessarily 0.
What is the difference between differentiation and integration?
Differentiation involves determination of the slope, i.e. the derivative, of a function. The slope of a function at a point is a straight line that is tangent to that function at that point, and is the line defined by the limit of two points on the original curve, one of those two points being the point in question, as their distance between each other becomes zero. There are several things you can do with derivatives, not the least of which is aid in plotting functions and finding various minima and maxima. Integration involves determination of the inverse-slope, i.e. the integral, of a function. The integral of a function is another function whose derivative is the first function. There are several things you can do with integrals, not the least of which is finding the area or volume under or in a curve or shape.
What is differentition?
Differentiation is just another way so saying find the derivative of a function.
What does the derivative of a function mean?
The derivative of a function is another function that represents the slope of the first function, slope being the limit of delta y over delta x at any two points x1,y1 and x2,y2 on the graph of the function as delta x approaches zero.
What is the relationship between a function and its derivative?
The derivative if a function is basically it's slope, or its rate of change. An example is the function y = 4x - 6. This is a line with a slope of 4. The derivative is y' = 4. Another example is the function y = 3x2. This is a parabola with a vertex at (0,0). Its derivative is y' = 6x. At x = 0, the slope of the parabola is 6*0, which is 0, since this is the vertex of the parabola. To the left, at x is -4 for example, the derivative (and therefore slope) is negative. To the right, at x = 5 for example, the derivative is positive. The farther away from the vertex, the greater the value of the derivative so the the slope of the function increases as you move away from the vertex (it gets steeper).
what is a derivative of a function?
Another function, which at every point has the value of the slope of the original function. For example, the parabola y = x2 has, at any point, the slope 2x, so 2x is the derivative of the original function. The Wikipedia article - http://en.wikipedia.org/wiki/Derivative - gives a more detailed introduction, but if you want to really learn about derivatives, you should pick up textbook on introductory calculus.
How do you find the derivative of y equals 7e-6x?
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How do you determine the relative minimum and relative maximum values of functions and the intervals on which functions are decreasing or increasing?
You take the derivative of the function. The derivative is another function that tells you the slope of the original function at any point. (If you don't know about derivatives already, you can learn the details on how to calculate in a calculus textbook. Or read the Wikipedia article for a brief introduction.) Once you have the derivative, you solve it for zero (derivative = 0). Any local maximum or minimum either has a derivative of zero, has no defined derivative, or is a border point (on the border of the interval you are considering). Now, as to the intervals where the function increase or decreases: Between any such maximum or minimum points, you take any random point and check whether the derivative is positive or negative. If it is positive, the function is increasing.
What is the integral of the quantity of the derivative with respect to x of the function f times another function of x defined as g subtracted by g prime times f divided by g squared with respect to x?
∫ [f'(x)g(x) - g'(x)f(x)]/g(x)2 dx = f(x)/g(x) + C C is the constant of integration.
What is the integral of 1 divided by the quantity of a function of x multiplied by the quantity of that same function plus or minus another function of x with respect to x?
∫ [1/[f(x)(f(x) ± g(x))]] dx = ±∫1/[f(x)g(x)] dx ± (-1)∫ [1/[g(x)(f(x) ± g(x))]] dx
