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  • Identical expressions

  • three ^tan(x)*arsin(x^ two)
  • 3 to the power of tangent of (x) multiply by ar sinus of (x squared )
  • three to the power of tangent of (x) multiply by ar sinus of (x to the power of two)
  • 3tan(x)*arsin(x2)
  • 3tanx*arsinx2
  • 3^tan(x)*arsin(x²)
  • 3 to the power of tan(x)*arsin(x to the power of 2)
  • 3^tan(x)arsin(x^2)
  • 3tan(x)arsin(x2)
  • 3tanxarsinx2
  • 3^tanxarsinx^2
The derivative of the function/ 3^tan(x)*arsin(x^2)

Derivative of 3^tan(x)*arsin(x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 tan(x)     / 2\
3      *asin\x /
$$3^{\tan{\left(x \right)}} \operatorname{asin}{\left(x^{2} \right)}$$ 
3^tan(x)*asin(x^2)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     tan(x)                                        
2*x*3          tan(x) /       2   \     / 2\       
----------- + 3      *\1 + tan (x)/*asin\x /*log(3)
   ________                                        
  /      4                                         
\/  1 - x
$$\frac{2 \cdot 3^{\tan{\left(x \right)}} x}{\sqrt{1 - x^{4}}} + 3^{\tan{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} \operatorname{asin}{\left(x^{2} \right)}$$
Simplify
The second derivative [src] 
        /    /          4 \                                                                                             \
        |    |       2*x  |                                                                                             |
        |  2*|-1 + -------|                                                                                             |
        |    |           4|                                                                         /       2   \       |
 tan(x) |    \     -1 + x /   /       2   \ /           /       2   \       \     / 2\          4*x*\1 + tan (x)/*log(3)|
3      *|- ---------------- + \1 + tan (x)/*\2*tan(x) + \1 + tan (x)/*log(3)/*asin\x /*log(3) + ------------------------|
        |       ________                                                                                 ________       |
        |      /      4                                                                                 /      4        |
        \    \/  1 - x                                                                                \/  1 - x         /
$$3^{\tan{\left(x \right)}} \left(\frac{4 x \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)}}{\sqrt{1 - x^{4}}} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} + 2 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} \operatorname{asin}{\left(x^{2} \right)} - \frac{2 \left(\frac{2 x^{4}}{x^{4} - 1} - 1\right)}{\sqrt{1 - x^{4}}}\right)$$
Simplify
The third derivative [src] 
        /       /          4 \                                                                                                                            /          4 \                                                                    \
        |     3 |       6*x  |                                                                                                              /       2   \ |       2*x  |                                                                    |
        |  4*x *|-5 + -------|                                                                                                            6*\1 + tan (x)/*|-1 + -------|*log(3)                                                             |
        |       |           4|                 /                             2                                        \                                   |           4|              /       2   \ /           /       2   \       \       |
 tan(x) |       \     -1 + x /   /       2   \ |         2      /       2   \     2        /       2   \              |     / 2\                          \     -1 + x /          6*x*\1 + tan (x)/*\2*tan(x) + \1 + tan (x)/*log(3)/*log(3)|
3      *|- ------------------- + \1 + tan (x)/*\2 + 6*tan (x) + \1 + tan (x)/ *log (3) + 6*\1 + tan (x)/*log(3)*tan(x)/*asin\x /*log(3) - ------------------------------------- + ----------------------------------------------------------|
        |              3/2                                                                                                                                ________                                          ________                        |
        |      /     4\                                                                                                                                  /      4                                          /      4                         |
        \      \1 - x /                                                                                                                                \/  1 - x                                         \/  1 - x                          /
$$3^{\tan{\left(x \right)}} \left(- \frac{4 x^{3} \left(\frac{6 x^{4}}{x^{4} - 1} - 5\right)}{\left(1 - x^{4}\right)^{\frac{3}{2}}} + \frac{6 x \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} + 2 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)}}{\sqrt{1 - x^{4}}} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(3 \right)}^{2} + 6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} \tan{\left(x \right)} + 6 \tan^{2}{\left(x \right)} + 2\right) \log{\left(3 \right)} \operatorname{asin}{\left(x^{2} \right)} - \frac{6 \left(\frac{2 x^{4}}{x^{4} - 1} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)}}{\sqrt{1 - x^{4}}}\right)$$
Simplify
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