It is worth giving one more piece of evidence for the formula above, this time based on increments in function, {{MATH_38}}, and increments in variable, {{MATH_39}}. Consider this plot of a function {{MATH_40}} and its inverse: {{CMD_41}} {{ENV_42}} {{COMMENT_43}} {{COMMENT_44}} {{COMMENT_45}} {{CMD_46}} Since the graph of the inverse of a function is the reflection of the graph of the function over the line {{MATH_47}}, we see that the increments are ``switched'' when reflected. Hence we see that {{MATH_48}} Taking the limit as {{MATH_49}} goes to {{MATH_50}}, we can obtain the expression for the derivative of {{MATH_51}}. {{CMD_52}} {{MATH_53}}