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How do you write derivatives in Wolfram Alpha?

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How do you write derivatives in Wolfram Alpha?

Derivative is generated when you apply D to functions whose derivatives the Wolfram Language does not know. The Wolfram Language attempts to convert Derivative[n][f] and so on to pure functions. Whenever Derivative[n][f] is generated, the Wolfram Language rewrites it as D[f[#],{#,n}]&.

Can Wolfram Alpha do derivatives?

More than just an online derivative solver Wolfram|Alpha is a great calculator for first, second and third derivatives; derivatives at a point; and partial derivatives.

What is a function f of two variables?

Definition 1 A function f of the two variables x and y is a rule that assigns a number f(x, y) to each point (x, y) in a portion or all of the xy-plane. f(x, y) is the value of the function at (x, y), and the set of points where the function is defined is called its domain.

What is the derivative of a variable?

The derivative of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x. It is called the derivative of f with respect to x.

How do you know if the second derivative is positive or negative?

The second derivative tells whether the curve is concave up or concave down at that point. If the second derivative is positive at a point, the graph is bending upwards at that point. Similarly if the second derivative is negative, the graph is concave down.

How to calculate a derivative in Wolfram Alpha?

How Wolfram|Alpha calculates derivatives. Wolfram|Alpha calls Wolfram Languages’s D function, which uses a table of identities much larger than one would find in a standard calculus textbook. It uses well-known rules such as the linearity of the derivative, product rule, power rule, chain rule and so on. Additionally, D uses lesser-known rules

What kind of system can Wolfram Alpha solve?

Wolfram|Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints.

How are differential equations solved in Wolfram Language?

Another approach for restructuring the system involves differentiating the original system number of times until the differentials for all the variables are accounted for. The preceding differentiated systems are treated as invariants. In order to solve the new index-reduced system, a consistent set of initial conditions must be found.

How are derivatives expressed in differential algebraic equations?

With differential-algebraic equations (DAEs), the derivatives are not, in general, expressed explicitly. In fact, derivatives of some of the dependent variables typically do not appear in the equations. For example, the following equation does not explicitly contain any derivatives of .