Section 3.2: Derivatives of Exponential and Logarithmic Functions

The Derivative of e^x

Calculating the derivative of e^x involves finding the limit of (e^h - 1)/h as h approaches zero.

Drag the slider to see the value of this expression for different values of h.

Derivatives of Exponential and Logarithmic Functions

For b > 0, b ≠ 1,

d/dx e^x = e^xandd/dx b^x = b^xln b

For b > 0, b ≠ 1, and x > 0

d/dx ln x = 1/xandd/dx log_b x = (1/ln b)(1/x)