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Maths Advanced

Derivative as the Gradient of the Tangent of the Graph

How is the derivative the gradient of the tangent of the graph?

In this post, we interpret the derivative as the gradient of the tangent to the graph of y=f(x) at a point x , as a part of the Prelim Maths Advanced course under the topic Calculus and sub-part The Derivative Function and its Graph. As the derivative tells us the rate of change of a function at any point, this is the exact same as the gradient of the tangent at any of the same points.

 

This video goes into further detail about how the derivative is interpreted as the slope of the tangent line, giving visual and graphical examples.