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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?
Wiki User
∙ 13y ago
∫ f'(x)/√[f(x)2 + a] dx = ln[f(x) + √(f(x)2 + a)] + C
C is the constant of integration.
Wiki User
∙ 13y ago
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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.
Constant is a quantity that does not?
Constant is a quantity that does not change.
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)
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 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)]
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 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.
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 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 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 f times g with respect to x?
∫ [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.
What is the integral of f prime divided by the quantity f times the square root of the quantity f squared minus a squared with respect to x where f is a function of x and a is a constant?
∫ f'(x)/[f(x)√(f(x)2 - a2)] dx = (1/a)arcses(f(x)/a) + C C is the constant of integration.
What quantity or expression has a derivative equal to zero?
Derivative of a constantThe derivative of any constant is zero. This can be easily conceptualized if you think of the graph of any constant value. The derivative can be thought of as the slope of the line tangent to a curve at any given point. If you graph the expression y = 3, for example, it is just a horizontal line intercepting the y axis at 3. The slope of that line is, of course, equal to zero, for any point on the curve (which in this case is a straight line). Therefore, the derivative (with respect to x) of y = 3 is zero. Since the slope of any horizontal line is zero, the derivative of any line of the form y = k, where k is a constant, is zero.Answer2:Any constant quantity and an expression that has a maximum or minimum or both, has a derivative equal to zero.
Does an exponential growth function represents a quantity that has a constant doubling time?
False
An exponential growth function represents a quantity that has a constant doubling time?
True
What is the integral of f prime divided by the square root of the quantity a squared minus f squared with respect to x where f is a function of x and a is a constant?
∫ f'(x)/√(a2 - f(x)2) dx = arcsin(f(x)/a) + C C is the constant of integration.
What is The rate of a changing quantity is the amount it changes per single increment of time?
The rate of a changing quantity is the derivative of that quantity with respect to time. It represents how fast the quantity is changing at a specific point in time. This rate can be constant or variable depending on the nature of the change.
Constant is a quantity that does not?
Constant is a quantity that does not change.
