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y=(x-4)^5arcctg(3x^2)
The derivative of the function/ y=(x-4)^5arcctg(3x^2)

Derivative of y=(x-4)^5arcctg(3x^2)

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

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       5     /   2\
(x - 4) *acot\3*x /
(x−4)5acot⁡(3x2)\left(x - 4\right)^{5} \operatorname{acot}{\left(3 x^{2} \right)} 
(x - 4)^5*acot(3*x^2)
The graph
02468-8-6-4-2-1010-50005000
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Plot the graph f'(x)
The first derivative [src] 
                                   5
         4     /   2\   6*x*(x - 4) 
5*(x - 4) *acot\3*x / - ------------
                                 4  
                          1 + 9*x
−6x(x−4)59x4+1+5(x−4)4acot⁡(3x2)- \frac{6 x \left(x - 4\right)^{5}}{9 x^{4} + 1} + 5 \left(x - 4\right)^{4} \operatorname{acot}{\left(3 x^{2} \right)}
Simplify
The second derivative [src] 
            /                                            /          4  \\
            |                                          2 |      36*x   ||
            |                                3*(-4 + x) *|-1 + --------||
            |                                            |            4||
          3 |       /   2\   30*x*(-4 + x)               \     1 + 9*x /|
2*(-4 + x) *|10*acot\3*x / - ------------- + ---------------------------|
            |                          4                      4         |
            \                   1 + 9*x                1 + 9*x          /
2(x−4)3(−30x(x−4)9x4+1+3(x−4)2(36x49x4+1−1)9x4+1+10acot⁡(3x2))2 \left(x - 4\right)^{3} \left(- \frac{30 x \left(x - 4\right)}{9 x^{4} + 1} + \frac{3 \left(x - 4\right)^{2} \left(\frac{36 x^{4}}{9 x^{4} + 1} - 1\right)}{9 x^{4} + 1} + 10 \operatorname{acot}{\left(3 x^{2} \right)}\right)
Simplify
The third derivative [src] 
            /                                             /          4  \                   /          4  \\
            |                                           2 |      36*x   |       3         3 |      72*x   ||
            |                                15*(-4 + x) *|-1 + --------|   36*x *(-4 + x) *|-5 + --------||
            |                                             |            4|                   |            4||
          2 |       /   2\   60*x*(-4 + x)                \     1 + 9*x /                   \     1 + 9*x /|
6*(-4 + x) *|10*acot\3*x / - ------------- + ---------------------------- - -------------------------------|
            |                          4                      4                                 2          |
            |                   1 + 9*x                1 + 9*x                        /       4\           |
            \                                                                         \1 + 9*x /           /
6(x−4)2(−36x3(x−4)3(72x49x4+1−5)(9x4+1)2−60x(x−4)9x4+1+15(x−4)2(36x49x4+1−1)9x4+1+10acot⁡(3x2))6 \left(x - 4\right)^{2} \left(- \frac{36 x^{3} \left(x - 4\right)^{3} \left(\frac{72 x^{4}}{9 x^{4} + 1} - 5\right)}{\left(9 x^{4} + 1\right)^{2}} - \frac{60 x \left(x - 4\right)}{9 x^{4} + 1} + \frac{15 \left(x - 4\right)^{2} \left(\frac{36 x^{4}}{9 x^{4} + 1} - 1\right)}{9 x^{4} + 1} + 10 \operatorname{acot}{\left(3 x^{2} \right)}\right)
Simplify
The graph
Derivative of y=(x-4)^5arcctg(3x^2)
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