# Derivatives of Exponential and Logarithmic Functions

##### 69 words — categories: calculus

The derivative of an exponential function of the form \(a^x\) is

\[\frac{d}{dx}a^x = (\ln a)a^x\]

```
from sympy import *
from sympy.abc import x
expr = 2**x
expr2 = 3**(2*x)
diff(expr)
```

`## 2**x*log(2)`

`diff(expr2)`

`## 2*3**(2*x)*log(3)`

The derivative of a function of the form \(\log_ax\)is

\[\frac{d}{dx}\log_a x = \frac{1}{\ln a} \cdot \frac{1}{x}\]

```
expr3 = log(x, 8)
expr4 = log((x**2 + 1), 3)
diff(expr3)
```

`## 1/(x*log(8))`

`diff(expr4)`

`## 2*x/((x**2 + 1)*log(3))`