f' represents the derivative of a function f of one argument. Derivative[n_1, n_2, ...][f] is the general form, representing a function obtained from f by differentiating n_1 ...

You can define the derivative in Mathematica of a function f of one argument simply by an assignment like f'[x_]=fp[x]. This defines the derivative of f(x) to be fp(x). In ...

Derivatives in Mathematica work essentially the same as in standard mathematics. The usual mathematical notation, however, often hides many details. To understand how ...

Total differentiation operations. When you find the derivative of some expression f with respect to x, you are effectively finding out how fast f changes as you vary x. Often ...

Differentiating a known function gives an explicit result. Differentiating an unknown function f gives a result in terms of f'. Mathematica applies the chain rule for ...

Mathematica makes it easy to take even the most complicated derivatives involving any of its huge range of differentiable special functions.

Dt[f, x] gives the total derivative d f/d x. Dt[f] gives the total differential d f. Dt[f, {x, n}] gives the multiple derivative d^n f/d x^n. Dt[f, x_1, x_2, ...] gives d/d ...

In calculus even more than other areas, Mathematica packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced ...

Partial differentiation operations. This gives ( ∂ ) / ( ∂x ) x^n. This gives the third derivative.

FinancialDerivative[instrument, params, ambientparams] gives the value of the specified financial instrument.FinancialDerivative[instrument, params, ambientparams, prop] ...