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y=3cosx/3*sin^215x/15cos30x
Derivada de la función/ y=3cosx/3*sin^215x/15cos30x

Derivada de y=3cosx/3*sin^215x/15cos30x

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src] 
3*cos(x)    215             
--------*sin   (x)          
   3                        
------------------*cos(30*x)
        15
3cos⁡(x)3sin⁡215(x)15cos⁡(30x)\frac{\frac{3 \cos{\left(x \right)}}{3} \sin^{215}{\left(x \right)}}{15} \cos{\left(30 x \right)} 
((((3*cos(x))/3)*sin(x)^215)/15)*cos(30*x)
Gráfica
02468-8-6-4-2-10100.1-0.1
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Primera derivada [src] 
/     216            2       214   \                                         
|  sin   (x)   43*cos (x)*sin   (x)|                  215                    
|- --------- + --------------------|*cos(30*x) - 2*sin   (x)*cos(x)*sin(30*x)
\      15               3          /
(−sin⁡216(x)15+43sin⁡214(x)cos⁡2(x)3)cos⁡(30x)−2sin⁡215(x)sin⁡(30x)cos⁡(x)\left(- \frac{\sin^{216}{\left(x \right)}}{15} + \frac{43 \sin^{214}{\left(x \right)} \cos^{2}{\left(x \right)}}{3}\right) \cos{\left(30 x \right)} - 2 \sin^{215}{\left(x \right)} \sin{\left(30 x \right)} \cos{\left(x \right)}
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Segunda derivada [src] 
            /                                                                             /           2             2   \                 \
     213    |        2                         /   2             2   \                    \- 23005*cos (x) + 323*sin (x)/*cos(x)*cos(30*x)|
2*sin   (x)*|- 30*sin (x)*cos(x)*cos(30*x) + 2*\sin (x) - 215*cos (x)/*sin(x)*sin(30*x) - ------------------------------------------------|
            \                                                                                                    15                       /
2(2(sin⁡2(x)−215cos⁡2(x))sin⁡(x)sin⁡(30x)−(323sin⁡2(x)−23005cos⁡2(x))cos⁡(x)cos⁡(30x)15−30sin⁡2(x)cos⁡(x)cos⁡(30x))sin⁡213(x)2 \left(2 \left(\sin^{2}{\left(x \right)} - 215 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \sin{\left(30 x \right)} - \frac{\left(323 \sin^{2}{\left(x \right)} - 23005 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)} \cos{\left(30 x \right)}}{15} - 30 \sin^{2}{\left(x \right)} \cos{\left(x \right)} \cos{\left(30 x \right)}\right) \sin^{213}{\left(x \right)}
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Tercera derivada [src] 
          //   4             2       2             2    /           2             2   \          2    /   2             2   \\                                                                                                                                                       \
   212    |\sin (x) - 645*cos (x)*sin (x) - 215*cos (x)*\- 45582*cos (x) + 643*sin (x)/ + 645*sin (x)*\sin (x) - 214*cos (x)//*cos(30*x)          2    /   2             2   \                     3                          /           2             2   \                        |
sin   (x)*|----------------------------------------------------------------------------------------------------------------------------- + 180*sin (x)*\sin (x) - 215*cos (x)/*cos(30*x) + 1800*sin (x)*cos(x)*sin(30*x) + 12*\- 23005*cos (x) + 323*sin (x)/*cos(x)*sin(x)*sin(30*x)|
          \                                                              15                                                                                                                                                                                                          /
(180(sin⁡2(x)−215cos⁡2(x))sin⁡2(x)cos⁡(30x)+12(323sin⁡2(x)−23005cos⁡2(x))sin⁡(x)sin⁡(30x)cos⁡(x)+(645(sin⁡2(x)−214cos⁡2(x))sin⁡2(x)−215(643sin⁡2(x)−45582cos⁡2(x))cos⁡2(x)+sin⁡4(x)−645sin⁡2(x)cos⁡2(x))cos⁡(30x)15+1800sin⁡3(x)sin⁡(30x)cos⁡(x))sin⁡212(x)\left(180 \left(\sin^{2}{\left(x \right)} - 215 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)} \cos{\left(30 x \right)} + 12 \left(323 \sin^{2}{\left(x \right)} - 23005 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \sin{\left(30 x \right)} \cos{\left(x \right)} + \frac{\left(645 \left(\sin^{2}{\left(x \right)} - 214 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)} - 215 \left(643 \sin^{2}{\left(x \right)} - 45582 \cos^{2}{\left(x \right)}\right) \cos^{2}{\left(x \right)} + \sin^{4}{\left(x \right)} - 645 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}\right) \cos{\left(30 x \right)}}{15} + 1800 \sin^{3}{\left(x \right)} \sin{\left(30 x \right)} \cos{\left(x \right)}\right) \sin^{212}{\left(x \right)}
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Gráfico
Derivada de y=3cosx/3*sin^215x/15cos30x
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