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The derivative of the function/ lnxsin3x

Derivative of lnxsin3x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x)*sin(3*x)
$$\log{\left(x \right)} \sin{\left(3 x \right)}$$ 
log(x)*sin(3*x)
Detail solution

  1. Apply the product rule:

    ; to find :

    1. The derivative of is .

    ; to find :

    1. Let .

    2. The derivative of sine is cosine:

    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 answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
sin(3*x)                    
-------- + 3*cos(3*x)*log(x)
   x
$$3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}$$
Simplify
The second derivative [src] 
  sin(3*x)                       6*cos(3*x)
- -------- - 9*log(x)*sin(3*x) + ----------
      2                              x     
     x
$$- 9 \log{\left(x \right)} \sin{\left(3 x \right)} + \frac{6 \cos{\left(3 x \right)}}{x} - \frac{\sin{\left(3 x \right)}}{x^{2}}$$
Simplify
The third derivative [src] 
  27*sin(3*x)                        9*cos(3*x)   2*sin(3*x)
- ----------- - 27*cos(3*x)*log(x) - ---------- + ----------
       x                                  2            3    
                                         x            x
$$- 27 \log{\left(x \right)} \cos{\left(3 x \right)} - \frac{27 \sin{\left(3 x \right)}}{x} - \frac{9 \cos{\left(3 x \right)}}{x^{2}} + \frac{2 \sin{\left(3 x \right)}}{x^{3}}$$
Simplify
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