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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.
How can one calculate marginal revenue from a demand curve?
To calculate marginal revenue from a demand curve, you can find the slope of the demand curve at a specific quantity using calculus or by taking the first derivative of the demand function. The marginal revenue is then equal to the price at that quantity minus the slope of the demand curve multiplied by the quantity.
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
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 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 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)
Marginal cost can be defined as the?
The cost of increasing the production by one unit. Mathematically, this can be derived as the derivative of the total costs with respect to quantity i.e. dc(q)/dq, where c(q) is the cost function and q is quantity.
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 the derivative with respect to x of f divided by the quantity q squared f squared minus p squared with respect to x where f is a function of x and p and q are constants?
∫ f'(x)/( q2f(x)2 - p2) dx = [1/(2pq)ln[(qf(x) - p)/(qf(x) + p)]
