which one of the following is an example of derivative?
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A derivative is an instrument whose value is derived from the value of one or more underlying, which can be commodities, precious metals, currency, bonds, stocks, stocks indices, etc. Four most common examples of derivative instruments are Forwards, Futures, Options and Swaps.
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More generally, if x0 is an interior point in the domain of a function f, then f is said to be differentiable at x0 if the derivative f ′(x0) exists. This means that the graph of f has a non-vertical tangent line at the point (x0, f(x0)).
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Tl;DR Limit calculates function value, derivative finds rate of change value. ... Say you have a function f(x), and say at x=a, f(a)=L. The "limit of the function" is the value the function approaches as x approaches a. Basically the closer x gets to a, the closer f(x) gets to L.
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The vertical tangent to a curve occurs at a point where the slope is undefined (infinite). This can also be explained in terms of calculus when the derivative at a point is undefined.
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The order of a differential equation is the order of the highest derivative that appears in the relation. The unknown function is called the dependent variable and the variable or variables on which it depend are the independent variables.
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How does the first derivative test differ from the second derivative test? ... The biggest difference is that the first derivative test always determines whether a function has a local maximum, a local minimum, or neither; however, the second derivative test fails to yield a conclusion when y'' is zero at a critical value.
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yes, dy/dx= 1/(dx/dy), when both are defined. It doesn't make sense to ask about it for partial derivatives in the manner you do.
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By the Sum Rule, the derivative of 8−x with respect to x is ddx[8]+ddx[−x] d d x [ 8 ] + d d x [ - x ] . Since 8 is constant with respect to x , the derivative of 8 with respect to x is 0 .
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The Difference Rule says that the derivative of a subtraction of functions is equal to the subtraction of each derivative. When finding the derivative of a function that has additions (+ ) and subtractions (− ), you need to get each derivative and keep the original sign for each term.
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A few examples of derivatives are futures, forwards, options and swaps. ... By using derivatives both parties agree on a sale at a specified price at a later date. In each derivative certain aspects are documented such as the relation between the derivative, type of underlying asset and the market in which they are traded.
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"Partial differentiation" is used when you have a function, say, f, of two independent variables, x and y. "Implicit differentiation" is used when you have a formula in two variable, such as x and y, and one variable, y, is a function of the other.
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A function is differentiable at a point when there's a defined derivative at that point. This means that the slope of the tangent line of the points from the left is approaching the same value as the slope of the tangent of the points from the right.
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While the first derivative can tell us if the function is increasing or decreasing, the second derivative. tells us if the first derivative is increasing or decreasing. If the second derivative is positive, then the first.
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Partial derivatives are typically independent of the order of differentiation, meaning Fxy = Fyx. ... For example, the first partial derivative Fx of the function f(x,y) = 3x^2*y - 2xy is 6xy - 2y. Calculate the derivative of the function with respect to y by determining d/dy (Fx), treating x as if it were a constant.
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A function is differentiable if it has a derivative. You can think of a derivative of a function as its slope. The relationship between continuous functions and differentiability is-- all differentiable functions are continuous but not all continuous functions are differentiable.
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The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².
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Velocity, being the first derivative of displacement, would be cos(t), which is 90 degrees out of phase. The second derivative of displacement (first derivative of velocity) is acceleration, -sin(t). This is an additional 90 degrees phase difference, for a total of 180 degrees, or Pi radians.