Learning Outcomes

  1. Find the derivative of exponential functions.
  2. Find the derivative of logarithmic functions.
  3. Use logarithmic differentiation to determine the derivative of a function.


  • Chapter 3.9  Derivatives of Exponential and Logarithmic Functions  

Textbook Assignment

  • p. 331:    331, 334, 337, 340, 341, 346, 347, 351

WeBWork Assignment

  • Derivatives-Exponential
  • Derivatives-Logarithms
  • Derivatives-Logarithmic

Exit problems of the session 

  1. Find the derivative  of the following functions:

    (a).  $y=3xe^{x^2}$    (b).   $y=2^{\sin x\cos x}$   (c).   $y=\ln(2x^3-x+1)$   (d).   $y=\log(\tan x)$
  2. Use logarithmic differentiation to find the derivative of the following functions. 
    (a).  $y=(2x)^{\sin x}$    (b).   $y=\dfrac{x^2\sqrt{2x+1}}{x^2-1}$


Key Concepts

  • Differentiation formulas for the exponential and logarithmic functions.


$\dfrac{d}{dx}(a^x)=a^x \ln a$

$\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}$

$\dfrac{d}{dx}(\log_a x)=\dfrac{1}{x\ln a}$

  • Logarithmic differentiation allows us to differentiate functions of the form  $y=f(x)^{g(x)}$  or very complex products or quotients by taking the natural logarithm of both sides and exploiting the properties of logarithms before differentiating. 


Videos and Practice Problems of Selected Topics

  1. $\rhd$ Derivative of exponential functions (5:24) Deriving the formula of the   derivative of $a^x$.
  2. $\rhd$ Derivative of logarithmic functions (4:47) Deriving the formula of the derivative of $\log_ax$.
  3. $\rhd$ An example (3:39) Find the derivative of $7^{x^2-x}$.
  4. $\rhd$ An example (4:09) Find the derivative of $\log_4(x^2+x)$.
  5. * Practice: Derivatives of $a^x$ and $\log_ax$. (4 problems)