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.

Textbook

  • 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}(e^x)=e^x

\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)