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Q: 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?

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âˆ« f'(x)/âˆš(af(x) + b) dx = 2âˆš(af(x) + b)/a + 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).

âˆ« f'(x)(af(x) + b)n dx = (af(x) + b)n + 1/[a(n + 1)] + C C is the constant of integration.

False

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Constant is a quantity that does not change.

âˆ« [f'(x)g(x) - g'(x)f(x)]/g(x)2 dx = f(x)/g(x) + C C is the constant of integration.

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.

âˆ« [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.

âˆ« f'(x)/[f(x)âˆš(f(x)2 - a2)] dx = (1/a)arcses(f(x)/a) + C C is the constant of integration.

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.

âˆ« f'(x)/âˆš(a2 - f(x)2) dx = arcsin(f(x)/a) + C C is the constant of integration.

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