Mister Exam

Other calculators

y=e^x*log5x
The derivative of the function/ y=e^x*log5x

Derivative of y=e^x*log5x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 x         
e *log(5*x)
$$e^{x} \log{\left(5 x \right)}$$ 
d / x         \
--\e *log(5*x)/
dx
$$\frac{d}{d x} e^{x} \log{\left(5 x \right)}$$
Transform
Detail solution

  1. Apply the product rule:

    ; to find :

    1. The derivative of is itself.

    ; 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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 x              
e     x         
-- + e *log(5*x)
x
$$e^{x} \log{\left(5 x \right)} + \frac{e^{x}}{x}$$
Simplify
The second derivative [src] 
/  1    2           \  x
|- -- + - + log(5*x)|*e 
|   2   x           |   
\  x                /
$$\left(\log{\left(5 x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x}$$
Simplify
The third derivative [src] 
/  3    2    3           \  x
|- -- + -- + - + log(5*x)|*e 
|   2    3   x           |   
\  x    x                /
$$\left(\log{\left(5 x \right)} + \frac{3}{x} - \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) e^{x}$$
Simplify
The graph
Derivative of y=e^x*log5x
    © Mister Exam – Calculator