The composition of these two mappings is a differentiable one-to-one mapping from computational space onto the domains or surfaces and has a nonvanishing Jacobian.
Let be a differentiable function on.
Let be a differentiable convex.
Also, let, be a differentiable function.
Let be a differentiable function, and let be its derivative.
For some equations, the higher order derivatives will reach 0. When y is a differentiable function of z, and z is a differentiable function of x, y is a composite function of x, and the derivative of y with respect to x (dy/dx) is (dy/du * du/dx).
Suppose that is a differentiable function.
When the variable is a differentiable function of the parameter, the sensitivity index may be alternatively defined using partial derivatives.
Theorem 13 Let E : R n → R n be a one-to-one and onto operator and let f be an E-differentiable function.
Theorem 26 Let E : R n → R n be a one-to-one and onto operator and let f : M ⊆ R n → R be an E-differentiable function.
