What does Differenciating mean?

What does Differenciating mean?

1 : the act or process of differentiating. 2 : development from the one to the many, the simple to the complex, or the homogeneous to the heterogeneous differentiation of Latin into vernaculars. 3 biology. a : modification of body parts for performance of particular functions.

What is basic differentiation rules?

CONSTANT FUNCTION RULE. A constant function is of the form f ( x ) = b where b is some real number. The derivative of ALL constant functions is always 0. Consider f ( x ) = 5 .

What is complex differentiation?

Complex Differentiation. The notion of the complex derivative is the basis of complex function theory. Complex differentiation is defined in the same manner as the usual calculus limit definition of the derivative of a real function. However, despite a superficial similarity, complex differentiation is a deeply different theory.

Are differentiation rules identical for functions of real and complex variables?

xz ations for functions of a real variable, we find practically all differentiation rules for functions of a complex variable turn out to be identical t o t 2 d f z gz f z g z dz d f zgz f zgz f zg z dz d f z gf fg dz g z g

How do you find the complex derivative of a function?

Theorem 1: A complex function f(z) = u(x, y) + iv(x, y) has a complex derivative f ′ (z) if and only if its real and imaginary part are continuously differentiable and satisfy the Cauchy-Riemann equations ux = vy, uy = − vx In this case, the complex derivative of f(z) is equal to any of the following expressions: f ′ (z)

Is a complex function differentiable at a point z 0 ∈ C?

A complex function f ( z) is differentiable at a point z 0 ∈ C if and only if the following limit difference quotient exists (1) f ′ ( z 0) = lim z → z 0 f ( z) − f ( z 0) z − z 0.