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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.
Equation for marginal cost and average cost?
Marginal cost - the derivative of the cost function with respect to quantity. Average cost - the cost function divided by quantity (q).
What is the rate of change of the quantity represented by the function d3x/dt3?
The rate of change of the quantity represented by the function d3x/dt3 is the third derivative of x with respect to t.
What is the integral of the derivative with respect to x of the function f divided by the square root of the quantity a times f plus b with respect to x?
∫ f'(x)/√(af(x) + b) dx = 2√(af(x) + b)/a + C C is the constant of integration.
What is the meaning of subtrahend?
A quantity or number to be subtracted from another.
What is the title or a number or quantity from which another is to be subtracted?
The minuend.
What are spacial derivatives?
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 is the integral of the derivative with respect to x of the function f divided by the square root of the quantity f squared plus a constant with respect to x?
∫ f'(x)/√[f(x)2 + a] dx = ln[f(x) + √(f(x)2 + a)] + C C is the constant of integration.
How do you calculate unit cost as you increase production?
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.
What is the integral of the derivative with respect to x of the function f multiplied by the quantity a times f plus b raised to the power of n with respect to x?
∫ f'(x)(af(x) + b)n dx = (af(x) + b)n + 1/[a(n + 1)] + C C is the constant of integration.
What is the integral of the derivative with respect to x of f divided by the quantity p squared plus q squared f squared with respect to x where f is a function of x and p and q are constants?
∫ f'(x)/(p2 + q2f(x)2) dx = [1/(pq)]arctan(qf(x)/p)
The ammount that remains after one quantity is subtracted from another?
the difference
