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What is the relationship of integral and differential calculus?
We say function F is an anti derivative, or indefinite integral of f if F' = f. Also, if f has an anti-derivative and is integrable on interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a) Thirdly, Let F(x) be the definite integral of integrable function f from a to x for all x in [a, b] of f, then F is an anti-derivative of f on [a,b] The definition of indefinite integral as anti-derivative, and the relation of definite integral with anti-derivative, we can conclude that integration and differentiation can be considered as two opposite operations.
How does calculus help us?
It is used in physics all the time. For example, acceleration is the derivative of velocity which is a derivative of position with respect to time. Calculating the amount of work done in a vector field (like an electrical field) also uses calculus.
Scientist who made calculus?
Newton is the named founder of Calculus. Yet there is controversy because it is claimed that Leibniz stole Newton's Calculus notes and took all credit for Calculus. But to this day Leibniz's integral and derivative notation is more commonly used that Newton's which was found confusing.
What is the fundamental theory of calculus?
The fundamental theorum of calculus states that a definite integral from a to b is equivalent to the antiderivative's expression of b minus the antiderivative expression of a.
Why was the calculus student confused about y equals ex and the derivative of y equals ex?
Because the derivative of e^x is e^x (the original function back again). This is the only function that has this behavior.
What does one use a Derivative Calculator for?
Derivative calculators are commonly used to help solve simple differential calculus equations. Generally, they are not able to solve complex calculus equations.
What is the relationship of integral and differential calculus?
We say function F is an anti derivative, or indefinite integral of f if F' = f. Also, if f has an anti-derivative and is integrable on interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a) Thirdly, Let F(x) be the definite integral of integrable function f from a to x for all x in [a, b] of f, then F is an anti-derivative of f on [a,b] The definition of indefinite integral as anti-derivative, and the relation of definite integral with anti-derivative, we can conclude that integration and differentiation can be considered as two opposite operations.
Derivative of log?
The derivative of a log is as follows: 1 divided by xlnb Where x is the number beside the log Where b is the base of the log and ln is just the natural log.
What is the calculus operation for finding the rate of change in an equation?
The calculus operation for finding the rate of change in an equation is differentiation. By taking the derivative of the equation, you can find the rate at which one variable changes with respect to another.
Scholar name for Proportional-Integral-Derivative method?
It is a one word name ; 'Calculus'.
How does calculus help us?
It is used in physics all the time. For example, acceleration is the derivative of velocity which is a derivative of position with respect to time. Calculating the amount of work done in a vector field (like an electrical field) also uses calculus.
What is the purpose of differential calculus?
Differential Calculus is to take the derivative of the function. It is important as it can be applied and supports other branches of science. For ex, If you have a velocity function, you can get its acceleration function by taking its derivative, same relationship as well with area and volume formulas.
Slope of an equation?
For a straight line (a linear equation), solve the equation for "y". That will give you an equation of the form: y = mx + b In this case, "m" is the slope (and "b" is the y-intercept). For an arbitrary equation, solve it for "y" again. Then you need to take the derivative. There are various rules for taking the derivative; you can see an overview in the Wikipedia article on "Derivative", but to understand the concept better, you should read an introductory calculus book.
What do all formulas in Calculus begin with?
There are lots of formulae in calculus, and they don't all begin the same way. Depending on what convention is used to express a derivative, the basic derivation formulae (which are BY NO MEANS all formulae used in calculus) usually start with d/dx, followed by some function or expression. In other words, "the derivative of ... is ...".
What is the derivative of pi divided by 2?
"Pi divided by 2" is a number, i.e. a constant. The derivative is the rate of change. The derivative of any constant is zero, because a constant never changes.
Whats the equation for slope?
If the algebraic equation is linear, in the form y = mx + b, the slope is simply m; the difference in y of any 2 points divided by the difference in x of those points (rise over run). If the equation is non-linear, the slope is the first derivative of that equation, from calculus. You woul need to know calculus to solve in this case. The slope will vary from point to point, unlike the linear case, where slope is constant.
How do you differentiate exponential function?
The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)
