∫ [f'(x)g(x) - g'(x)f(x)]/g(x)2 dx = f(x)/g(x) + C
C is the constant of integration.
0
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.
True!
∫ f(x)/[(f(x) + b)(f(x) + c)] dx = [b/(b - c)] ∫ 1/(f(x) + b) dx - [c/(b - c)] ∫ 1/(f(x) + c) dx b ≠c
∫ [f'(x)g(x) - f(x)g'(x)]/(f(x)2 + g(x)2) dx = arctan(f(x)/g(x)) + C C is the constant of integration.
∫ [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.
Marginal cost - the derivative of the cost function with respect to quantity. Average cost - the cost function divided by quantity (q).
The rate of change of the quantity represented by the function d3x/dt3 is the third derivative of x with respect to t.
∫ f'(x)/√(af(x) + b) dx = 2√(af(x) + b)/a + C C is the constant of integration.
A quantity or number to be subtracted from another.
The minuend.
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.
∫ f'(x)/√[f(x)2 + a] dx = ln[f(x) + √(f(x)2 + a)] + C C is the constant of integration.
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.
∫ f'(x)(af(x) + b)n dx = (af(x) + b)n + 1/[a(n + 1)] + C C is the constant of integration.
∫ f'(x)/(p2 + q2f(x)2) dx = [1/(pq)]arctan(qf(x)/p)
the difference