#Derivative of Exponential and Logarithmic Functions

#Table of Contents

1. Derivative of the Exponential Function
   • Differentiating $e^x$
   • Differentiating $e^{kx}$
   • Differentiating $a e^{kx}$
   • Worked Example
2. Derivative of a Number Raised to the Power of x
   • Differentiating $a^x$
   • Differentiating $a^{kx}$
   • Worked Example
3. Derivative of the Natural Logarithmic Function
   • Differentiating $\ln x$
   • Differentiating $a \ln x$
   • Differentiating $\ln kx$
   • Worked Example
4. Practice Questions
5. Glossary
6. Summary and Key Takeaways

#Derivative of the Exponential Function

#Differentiating $e^x$

The function $f(x) = e^x$ is unique because its rate of change is equal to itself.

$$f'(x) = e^x$$

#Differentiating $e^{kx}$

For the function $g(x) = e^{kx}$, its rate of change is proportional to itself.

$$g'(x) = k e^{kx}$$

This result is due to the chain rule.

#Differentiating $a e^{kx}$

For a function with a constant multiple of the exponential, the differentiation fo...