# Derivative of bases other than e

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Derivative of bases other than e : To differentiate exponential and logarithmic functions to other bases, you have three options:
(1) use the definitions of $a^{x} and \log_{a}{x}$ and differentiate using the rules for the natural exponential and logarithmic functions.
(2) use logarithmic differentiation, or
(3) use the differentiation rules for bases other than given in the theorem below.

Let 'a' be any positive real number and 'u' be a differentiable function of x.
1) $\frac{\text{d}}{\text{d}x}(a^{x}) = a^{x}. ln(a)$

2) $\frac{\text{d}}{\text{d}x}(a^{u}) = a^{u}. ln(a).\frac{\text{d}u}{\text{d}x}$

2) $\frac{\text{d}}{\text{d}x}(\log_{a}{x})= \frac{1}{ln(a).x}$

3) $\frac{\text{d}}{\text{d}x}(\log_{a}{u})= \frac{1}{ln(a).u}\frac{\text{d}u}{\text{d}x}$