31. Be a " k " times differentiable function at the point. 32. For unconstrained problems with twice-differentiable functions, some locally Lipschitz functions. 33. In other words, a differentiable curve differentiable manifold is of dimension one. 34. In other words, a differentiable curve differentiable manifold is of dimension one. 35. Another way to define orientations on a differentiable manifold is through volume forms. 36. Derivatives of compositions involving differentiable functions can be found using the chain rule. 37. If a function is differentiable and convex then it is also continuously differentiable. 38. If a function is differentiable and convex then it is also continuously differentiable . 39. Informally, this means that differentiable functions are very atypical among continuous functions. 40. Suppose that the functions are continuously differentiable with derivatives.
