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The derivative of the function/ 3x^(cosecx)

Derivative of 3x^(cosecx)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
   cos(E)*c*x
3*x
3xxccos⁡(e)3 x^{x c \cos{\left(e \right)}} 
3*x^((cos(E)*c)*x)
Detail solution

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

    1. Don't know the steps in finding this derivative.

      But the derivative is

      (xccos⁡(e))xccos⁡(e)(log⁡(xccos⁡(e))+1)\left(x c \cos{\left(e \right)}\right)^{x c \cos{\left(e \right)}} \left(\log{\left(x c \cos{\left(e \right)} \right)} + 1\right)

    So, the result is: 3(xccos⁡(e))xccos⁡(e)(log⁡(xccos⁡(e))+1)3 \left(x c \cos{\left(e \right)}\right)^{x c \cos{\left(e \right)}} \left(\log{\left(x c \cos{\left(e \right)} \right)} + 1\right)

  2. Now simplify:

    3(cxcos⁡(e))cxcos⁡(e)(log⁡(cxcos⁡(e))+1)3 \left(c x \cos{\left(e \right)}\right)^{c x \cos{\left(e \right)}} \left(\log{\left(c x \cos{\left(e \right)} \right)} + 1\right)

The answer is:

3(cxcos⁡(e))cxcos⁡(e)(log⁡(cxcos⁡(e))+1)3 \left(c x \cos{\left(e \right)}\right)^{c x \cos{\left(e \right)}} \left(\log{\left(c x \cos{\left(e \right)} \right)} + 1\right)

The first derivative [src] 
   cos(E)*c*x                             
3*x          *(c*cos(E) + c*cos(E)*log(x))
3xxccos⁡(e)(clog⁡(x)cos⁡(e)+ccos⁡(e))3 x^{x c \cos{\left(e \right)}} \left(c \log{\left(x \right)} \cos{\left(e \right)} + c \cos{\left(e \right)}\right)
Simplify
The second derivative [src] 
     c*x*cos(E) /1                 2       \       
3*c*x          *|- + c*(1 + log(x)) *cos(E)|*cos(E)
                \x                         /
3cxcxcos⁡(e)(c(log⁡(x)+1)2cos⁡(e)+1x)cos⁡(e)3 c x^{c x \cos{\left(e \right)}} \left(c \left(\log{\left(x \right)} + 1\right)^{2} \cos{\left(e \right)} + \frac{1}{x}\right) \cos{\left(e \right)}
Simplify
The third derivative [src] 
     c*x*cos(E) /  1     2             3    2      3*c*(1 + log(x))*cos(E)\       
3*c*x          *|- -- + c *(1 + log(x)) *cos (E) + -----------------------|*cos(E)
                |   2                                         x           |       
                \  x                                                      /
3cxcxcos⁡(e)(c2(log⁡(x)+1)3cos⁡2(e)+3c(log⁡(x)+1)cos⁡(e)x−1x2)cos⁡(e)3 c x^{c x \cos{\left(e \right)}} \left(c^{2} \left(\log{\left(x \right)} + 1\right)^{3} \cos^{2}{\left(e \right)} + \frac{3 c \left(\log{\left(x \right)} + 1\right) \cos{\left(e \right)}}{x} - \frac{1}{x^{2}}\right) \cos{\left(e \right)}
Simplify
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