Derivative of exponential functions

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. ddx  2x\frac{d}{{dx}}\;{2^x}
    ddx  24x3\frac{d}{{dx}}\;{2^{4{x^3}}}
?
Examples
Lessons
  1. ddx  35x2\frac{d}{{dx}}\;{3^{{5^{{x^2}}}}}
    1. ddx  ex\frac{{d}}{{{d}x}}\;{{e}^x}
      ddx  esin⁡x\frac{{d}}{{{d}x}}\;{{e}^{\sin x}}
      1. Differentiate:
        y=tan  (  cos⁡e5x2  )y = {tan\;}(\;\cos {{e}^{5{x^2}}}\;)
        1. ddx  x5\frac{d}{{dx}}\;{x^5} VS. ddx  5x\frac{d}{{dx}}\;{5^x}
          Topic Notes
          ?
          An exponential function is a function containing a numerical base with at least one variable in its exponent. In this section, we will learn how to differentiate exponential functions, including natural exponential functions and other composite functions that require the application of the Chain Rule.
          Differential Rules – Exponential Functions

          ddx  cx=cx⋅ln⁡c\frac{{d}}{{{d}x}}\;{c^x} = {c^x} \cdot \ln c
          ddx  c(        )=c(        )⋅ln⁡c⋅ddx(        )\frac{{d}}{{{d}x}}\;{c^{\left( {\;\;\;\;} \right)}} = {c^{\left( {\;\;\;\;} \right)}} \cdot \ln c \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)


          ddx  ex=ex\frac{{d}}{{{d}x}}\;{{e}^x} = {{e}^x}
          ddx  e(        )=e(        )⋅ddx(        )\frac{{d}}{{{d}x}}\;{{e}^{\left( {\;\;\;\;} \right)}} = {{e}^{\left( {\;\;\;\;} \right)}} \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)