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continuously differentiable

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1: 18.32 OP’s with Respect to Freud Weights
where Q ( x ) is real, even, nonnegative, and continuously differentiable. …
2: 4.12 Generalized Logarithms and Exponentials
Both ϕ ( x ) and ψ ( x ) are continuously differentiable. …
3: 1.4 Calculus of One Variable
If f ( n ) exists and is continuous on an interval I , then we write f C n ( I ) . When n 1 , f is continuously differentiable on I . … … A continuously differentiable function is convex iff the curve does not lie below its tangent at any point. …
4: 1.6 Vectors and Vector-Valued Functions
when f is continuously differentiable. … For x , y , and z continuously differentiable, the vectors … when F is a continuously differentiable vector-valued function. … when F is a continuously differentiable vector-valued function. … For f and g twice-continuously differentiable functions …
5: 1.5 Calculus of Two or More Variables
The function f ( x , y ) is continuously differentiable if f , f / x , and f / y are continuous, and twice-continuously differentiable if also 2 f / x 2 , 2 f / y 2 , 2 f / x y , and 2 f / y x are continuous. …
1.5.6 2 f x y = 2 f y x .
If F ( x , y ) is continuously differentiable, F ( a , b ) = 0 , and F / y 0 at ( a , b ) , then in a neighborhood of ( a , b ) , that is, an open disk centered at a , b , the equation F ( x , y ) = 0 defines a continuously differentiable function y = g ( x ) such that F ( x , g ( x ) ) = 0 , b = g ( a ) , and g ( x ) = - F x / F y . … If f is n + 1 times continuously differentiable, then … Sufficient conditions for validity are: (a) f and f / x are continuous on a rectangle a x b , c y d ; (b) when x [ a , b ] both α ( x ) and β ( x ) are continuously differentiable and lie in [ c , d ] . …
6: 1.8 Fourier Series
Suppose that f ( x ) is twice continuously differentiable and f ( x ) and | f ′′ ( x ) | are integrable over ( - , ) . …
7: 9.11 Products
For any continuously-differentiable function f
8: 30.14 Wave Equation in Oblate Spheroidal Coordinates
If b 1 = b 2 = 0 , then the function (30.13.8) is a twice-continuously differentiable solution of (30.13.7) in the entire ( x , y , z ) -space. …
9: 2.7 Differential Equations
In a finite or infinite interval ( a 1 , a 2 ) let f ( x ) be real, positive, and twice-continuously differentiable, and g ( x ) be continuous. …has twice-continuously differentiable solutions …
10: 3.8 Nonlinear Equations
This is an iterative method for real twice-continuously differentiable, or complex analytic, functions: …