When I found the formula of differentiation and by imagining the graph of it I was able to find that the formula gives us the tangent of the curve at the point where the curve is differentiated. Let us discuss about it in detail.
Look at the picture above. We find the when the point Q moves closer and and closer to P along the curve the secant PQ becomes a tangent at P i.e. PT. This happens when y _{1} tends to y_{0} and x_{1} tends to x_{0}. In graphical terms we write this as y_{1} → y_{0} and x_{1} → x_{0}.When these points becomes very close then the value of y_{1} − y_{0} and x_{1} − x_{0} becomes infinitely small and y_{1} − y_{0} = δ and x_{1} − x_{0} = ε. This δ/ε gives the slope of the tangent.From the previous post, change in y = Δy and change in x = Δx This Δy and Δx can be written as δy and δx as the value of both the quantities become infinitely small. |

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