A derivative is the rate of change of a function with respect to an independent variable (usually time or just x). For example, the derivative of a position-versus-time graph (with the independent variable being time) is the rate of change of position as time passes. This is the velocity-versus-time graph. Similarly, the derivative of the velocity-versus-time graph is the acceleration-versus-time graph.
Here's another way to think about the derivative of a function. If you were to record the slopes of the tangent lines to each point on a graph, then put those values on a different graph, you would create a graph of the derivative of the original function. In other words, you would have found every instantaneous rate of change of the original function and graphed it in their own function.
Chat with our AI personalities
Derivation of x2 or 2x is 2.
The derivation of the formula of pyramid can be gained easily based on the formula for a triangular prism. A pyramid is like two prisms joined together.
applied in making of aeroplane wings
Integration results in an equation which gives the area under the original equation between the bounds. Derivation results in an equation which gives the slope of the original line at any point.
See wikipedia article on polytropic processes.