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y=e^(3x)*log8x

Derivative of y=e^(3x)*log8x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 3*x         
E   *log(8*x)
$$e^{3 x} \log{\left(8 x \right)}$$
E^(3*x)*log(8*x)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Let .

    2. The derivative of is itself.

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

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    ; to find :

    1. Let .

    2. The derivative of is .

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

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 3*x                  
e         3*x         
---- + 3*e   *log(8*x)
 x                    
$$3 e^{3 x} \log{\left(8 x \right)} + \frac{e^{3 x}}{x}$$
The second derivative [src]
/  1    6             \  3*x
|- -- + - + 9*log(8*x)|*e   
|   2   x             |     
\  x                  /     
$$\left(9 \log{\left(8 x \right)} + \frac{6}{x} - \frac{1}{x^{2}}\right) e^{3 x}$$
The third derivative [src]
/  9    2    27              \  3*x
|- -- + -- + -- + 27*log(8*x)|*e   
|   2    3   x               |     
\  x    x                    /     
$$\left(27 \log{\left(8 x \right)} + \frac{27}{x} - \frac{9}{x^{2}} + \frac{2}{x^{3}}\right) e^{3 x}$$
The graph
Derivative of y=e^(3x)*log8x