This line is tangent to the graph of E(x)=e^x at x=0. The graph of E(x)=e^x together with the line y=x+1 are shown in (Figure). The evidence from the table suggests that 2.71820, is defined for every real number and is continuous. Well try to figure out the derivative of the natural logarithm function ln. As we develop these formulas, we need to make certain basic assumptions. The inverse of the exponential function y c x is the logarithmic function x log c (y). The constant value c becomes the base, and the variable x is the exponent to which c is raised. The roles of the variable and the constant value have changed places. Just as when we found the derivatives of other functions, we can find the derivatives of exponential and logarithmic functions using formulas. Exponential functions take the form (x) c x.
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