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Q: 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?

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A spacial derivativeis a measure of how a quantity is changing in space. This is in contrast to a temporal derivative which would be a measure of how a quantity is changing in time.For instance, is you placed a metal bar with one end in ice water, and the other end in boiling water, you could measure the temperature along the bar. The temperature would be different at each point along the bar. The rate of change of this temperature along the bar is a spacial derivative.(A temporal derivative would be if you took a hot piece of metal and put one end in ice, then measured the temperature at the other end over time, and found the rate at which it cools down.)In mathematics it is usual, if given some function F, to denote spacial derivatives as dF/dx, dF/dy, dF/dz, or Fx, Fy, Fz, when dealing with normal Cartesian coordinates.

In general, if you're taking the derivative with respect to X, then you take the current power of X, multiply the given quantity by that number and then subtract one from the current power. In this case, that's an overcomplicated way of describing what happens but here's the process: 5x is more fully 5*x^1 So you take the power (1) and multiply it it by the given quantity. This gives you 1*5*x^1 Now you subtract one from the current power giving you 1*5*x^0 which equals 5. So the answer is simply 5 in this case. But what if you were trying to find the derivative of 4x^7? In this case, you would multiply the quantity by 7 (giving you 7*4*x^7) and subtract 1 from the current power giving you a final answer of 28*x^6. This also works for negative powers and square roots. The derivative of sqrt(x) can be found by recognizing that this is equal to x^(1/2). So you multiply everything by 1/2 and subtract one from the power and get 1/2 * x^(-1/2) which equals 1/2 * 1/sqrt(x) = 1/(2*sqrt(x))

âˆ« f(x)/[(f(x) + b)(f(x) + c)] dx = [b/(b - c)] âˆ« 1/(f(x) + b) dx - [c/(b - c)] âˆ« 1/(f(x) + c) dx b â‰ c

Related questions

Marginal cost - the derivative of the cost function with respect to quantity. Average cost - the cost function divided by quantity (q).

âˆ« [f'(x)g(x) - g'(x)f(x)]/[f(x)g(x)] dx = ln(f(x)/g(x)) + C C is the constant of integration.

The minuend.

A quantity or number to be subtracted from another.

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.

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.

âˆ« f'(x)/âˆš(af(x) + b) dx = 2âˆš(af(x) + b)/a + C C is the constant of integration.

The quantity subtracted.

the difference

Increase in cost: take the first derivative with respect to the unit produced of a cost function. Total cost: sub-in the new quantity into the cost function.

To have taken away a quantity from another i.e. subtracted

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