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(x^3+4)^tan(x)
The derivative of the function/ (x^3+4)^tan(x)

Derivative of (x^3+4)^tan(x)

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

from to

Piecewise:

The solution

You have entered [src] 
        tan(x)
/ 3    \      
\x  + 4/
(x3+4)tan⁡(x)\left(x^{3} + 4\right)^{\tan{\left(x \right)}} 
(x^3 + 4)^tan(x)
Detail solution

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

    But the derivative is

    (log⁡(tan⁡(x))+1)tan⁡tan⁡(x)(x)\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}

The answer is:

(log⁡(tan⁡(x))+1)tan⁡tan⁡(x)(x)\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}

The graph
02468-8-6-4-2-10102e38-1e38
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        tan(x) /                               2       \
/ 3    \       |/       2   \    / 3    \   3*x *tan(x)|
\x  + 4/      *|\1 + tan (x)/*log\x  + 4/ + -----------|
               |                                3      |
               \                               x  + 4  /
(x3+4)tan⁡(x)(3x2tan⁡(x)x3+4+(tan⁡2(x)+1)log⁡(x3+4))\left(x^{3} + 4\right)^{\tan{\left(x \right)}} \left(\frac{3 x^{2} \tan{\left(x \right)}}{x^{3} + 4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right)
Simplify
The second derivative [src] 
               /                                         2                                                                                     \
        tan(x) |/                               2       \       4                                                               2 /       2   \|
/     3\       ||/       2   \    /     3\   3*x *tan(x)|    9*x *tan(x)     /       2   \    /     3\          6*x*tan(x)   6*x *\1 + tan (x)/|
\4 + x /      *||\1 + tan (x)/*log\4 + x / + -----------|  - ----------- + 2*\1 + tan (x)/*log\4 + x /*tan(x) + ---------- + ------------------|
               ||                                    3  |             2                                                3                3      |
               |\                               4 + x   /     /     3\                                            4 + x            4 + x       |
               \                                              \4 + x /                                                                         /
(x3+4)tan⁡(x)(−9x4tan⁡(x)(x3+4)2+6x2(tan⁡2(x)+1)x3+4+6xtan⁡(x)x3+4+(3x2tan⁡(x)x3+4+(tan⁡2(x)+1)log⁡(x3+4))2+2(tan⁡2(x)+1)log⁡(x3+4)tan⁡(x))\left(x^{3} + 4\right)^{\tan{\left(x \right)}} \left(- \frac{9 x^{4} \tan{\left(x \right)}}{\left(x^{3} + 4\right)^{2}} + \frac{6 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3} + 4} + \frac{6 x \tan{\left(x \right)}}{x^{3} + 4} + \left(\frac{3 x^{2} \tan{\left(x \right)}}{x^{3} + 4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \tan{\left(x \right)}\right)
Simplify
The third derivative [src] 
               /                                         3                                                                                                                                                                                                                                                                                                                           \
        tan(x) |/                               2       \                   2                 /                               2       \ /     4                                                               2 /       2   \\                  3              4 /       2   \                                              /       2   \       6              2 /       2   \       |
/     3\       ||/       2   \    /     3\   3*x *tan(x)|      /       2   \     /     3\     |/       2   \    /     3\   3*x *tan(x)| |  9*x *tan(x)     /       2   \    /     3\          6*x*tan(x)   6*x *\1 + tan (x)/|   6*tan(x)   54*x *tan(x)   27*x *\1 + tan (x)/        2    /       2   \    /     3\   18*x*\1 + tan (x)/   54*x *tan(x)   18*x *\1 + tan (x)/*tan(x)|
\4 + x /      *||\1 + tan (x)/*log\4 + x / + -----------|  + 2*\1 + tan (x)/ *log\4 + x / + 3*|\1 + tan (x)/*log\4 + x / + -----------|*|- ----------- + 2*\1 + tan (x)/*log\4 + x /*tan(x) + ---------- + ------------------| + -------- - ------------ - ------------------- + 4*tan (x)*\1 + tan (x)/*log\4 + x / + ------------------ + ------------ + --------------------------|
               ||                                    3  |                                     |                                    3  | |           2                                                3                3      |         3             2                  2                                                         3                  3                    3          |
               |\                               4 + x   /                                     \                               4 + x   / |   /     3\                                            4 + x            4 + x       |    4 + x      /     3\           /     3\                                                     4 + x           /     3\                4 + x           |
               \                                                                                                                        \   \4 + x /                                                                         /               \4 + x /           \4 + x /                                                                     \4 + x /                                /
(x3+4)tan⁡(x)(54x6tan⁡(x)(x3+4)3−27x4(tan⁡2(x)+1)(x3+4)2−54x3tan⁡(x)(x3+4)2+18x2(tan⁡2(x)+1)tan⁡(x)x3+4+18x(tan⁡2(x)+1)x3+4+(3x2tan⁡(x)x3+4+(tan⁡2(x)+1)log⁡(x3+4))3+3(3x2tan⁡(x)x3+4+(tan⁡2(x)+1)log⁡(x3+4))(−9x4tan⁡(x)(x3+4)2+6x2(tan⁡2(x)+1)x3+4+6xtan⁡(x)x3+4+2(tan⁡2(x)+1)log⁡(x3+4)tan⁡(x))+2(tan⁡2(x)+1)2log⁡(x3+4)+4(tan⁡2(x)+1)log⁡(x3+4)tan⁡2(x)+6tan⁡(x)x3+4)\left(x^{3} + 4\right)^{\tan{\left(x \right)}} \left(\frac{54 x^{6} \tan{\left(x \right)}}{\left(x^{3} + 4\right)^{3}} - \frac{27 x^{4} \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{3} + 4\right)^{2}} - \frac{54 x^{3} \tan{\left(x \right)}}{\left(x^{3} + 4\right)^{2}} + \frac{18 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{3} + 4} + \frac{18 x \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3} + 4} + \left(\frac{3 x^{2} \tan{\left(x \right)}}{x^{3} + 4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right)^{3} + 3 \left(\frac{3 x^{2} \tan{\left(x \right)}}{x^{3} + 4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right) \left(- \frac{9 x^{4} \tan{\left(x \right)}}{\left(x^{3} + 4\right)^{2}} + \frac{6 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3} + 4} + \frac{6 x \tan{\left(x \right)}}{x^{3} + 4} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \tan{\left(x \right)}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x^{3} + 4 \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \tan^{2}{\left(x \right)} + \frac{6 \tan{\left(x \right)}}{x^{3} + 4}\right)
Simplify
The graph
Derivative of (x^3+4)^tan(x)
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