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9^(x-1)
The derivative of the function/ 9^(x-1)

Derivative of 9^(x-1)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 x - 1
9
$$9^{x - 1}$$ 
d / x - 1\
--\9     /
dx
$$\frac{d}{d x} 9^{x - 1}$$
Transform
Detail solution

  1. Let .

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 x - 1       
9     *log(9)
$$9^{x - 1} \log{\left(9 \right)}$$
Simplify
The second derivative [src] 
 x    2   
9 *log (9)
----------
    9
$$\frac{9^{x} \log{\left(9 \right)}^{2}}{9}$$
Simplify
The third derivative [src] 
 x    3   
9 *log (9)
----------
    9
$$\frac{9^{x} \log{\left(9 \right)}^{3}}{9}$$
Simplify
The graph
Derivative of 9^(x-1)
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