umatisi6ar

2023-03-11

What is the derivative of $f\left(x\right)={b}^{x}$?

Edward Hunter

Beginner2023-03-12Added 5 answers

This is the exponential function of base b (where $b>0$ should be assumed). It can be thought of as $b}^{x}={e}^{x\mathrm{ln}\left(b\right)$, therefore, using the Chain Rule (See Chain Rule ) and the fact that $\left({e}^{x}\right)\prime ={e}^{x}$ (see Exponentials with Base e ) yields $\left({b}^{x}\right)\prime ={e}^{x\mathrm{ln}\left(b\right)}\times \mathrm{ln}\left(b\right)={b}^{x}\times \mathrm{ln}\left(b\right)$

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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