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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.10%3A_Chapter_3_Review_ExercisesThis page contains exercises on calculus derivatives, including evaluating derivatives, proving statements, and deriving tangent line equations. It emphasizes the interpretation of derivatives in prac...This page contains exercises on calculus derivatives, including evaluating derivatives, proving statements, and deriving tangent line equations. It emphasizes the interpretation of derivatives in practical contexts like water levels and wind speeds. The answer sections illustrate the connection between mathematical calculations and real-world applications by providing derivative functions and their evaluations at specific points.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_FunctionThe derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive ...The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/05%3A_The_Laplace_Transform/5.02%3A_Transforms_of_Derivatives_and_ODEsThe procedure for linear constant coefficient equations is as follows. We take an ordinary differential equation in the time variable t . We apply the Laplace transform to transform the equation into ...The procedure for linear constant coefficient equations is as follows. We take an ordinary differential equation in the time variable t . We apply the Laplace transform to transform the equation into an algebraic (non differential) equation in the frequency domain. We solve the equation for X(s) . Then taking the inverse transform, if possible, we find x(t). Unfortunately, not every function has a Laplace transform, not every equation can be solved in this manner.
