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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?
Mrkbh
∫ [f'(x)g(x) - g'(x)f(x)]/g(x)2 dx = f(x)/g(x) + C
C is the constant of integration.
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∙ 13y ago
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What is 5y- 5y?
0
What are spatial derivatives?
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.
Is the quantity represented by x is a function that changes over time ie is not constant true or false?
True!
How do you find the derivative of 5x?
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))
What is the integral of f divided by the quantity f plus b times f plus c with respect to x where f is a function of x and b and c are constants?
∫ 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
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.
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 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 title or a number or quantity from which another is to be subtracted?
The minuend.
What is the meaning of subtrahend?
A quantity or number to be subtracted from another.
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.
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.
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)
What does the words decreased by mean in an operation in math?
The quantity subtracted.
The ammount that remains after one quantity is subtracted from another?
the difference
