Mister Exam

Derivative of xlog10x+2^x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
               x
x*log(10*x) + 2 
$$2^{x} + x \log{\left(10 x \right)}$$
d /               x\
--\x*log(10*x) + 2 /
dx                  
$$\frac{d}{d x} \left(2^{x} + x \log{\left(10 x \right)}\right)$$
Detail solution
  1. Differentiate term by term:

    1. Apply the product rule:

      ; to find :

      1. Apply the power rule: goes to

      ; 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:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     x                   
1 + 2 *log(2) + log(10*x)
$$2^{x} \log{\left(2 \right)} + \log{\left(10 x \right)} + 1$$
The second derivative [src]
1    x    2   
- + 2 *log (2)
x             
$$2^{x} \log{\left(2 \right)}^{2} + \frac{1}{x}$$
The third derivative [src]
  1     x    3   
- -- + 2 *log (2)
   2             
  x              
$$2^{x} \log{\left(2 \right)}^{3} - \frac{1}{x^{2}}$$
The graph
Derivative of xlog10x+2^x