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y=cos(sin^4(x^2-4x))
Derivada de la función/ y=cos/ x^2-4/ sin^4/ y=cos(sin^4(x^2-4x))

Derivada de y=cos(sin^4(x^2-4x))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
   /   4/ 2      \\
cos\sin \x  - 4*x//
cos⁡(sin⁡4(x2−4x))\cos{\left(\sin^{4}{\left(x^{2} - 4 x \right)} \right)} 
cos(sin(x^2 - 4*x)^4)
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      3/ 2      \               / 2      \    /   4/ 2      \\
-4*sin \x  - 4*x/*(-4 + 2*x)*cos\x  - 4*x/*sin\sin \x  - 4*x//
−4(2x−4)sin⁡3(x2−4x)sin⁡(sin⁡4(x2−4x))cos⁡(x2−4x)- 4 \left(2 x - 4\right) \sin^{3}{\left(x^{2} - 4 x \right)} \sin{\left(\sin^{4}{\left(x^{2} - 4 x \right)} \right)} \cos{\left(x^{2} - 4 x \right)}
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Segunda derivada [src] 
     2             /                     /   4            \                             2    2                /   4            \             2    2                /   4            \             2    2                4                /   4            \\
8*sin (x*(-4 + x))*\- cos(x*(-4 + x))*sin\sin (x*(-4 + x))/*sin(x*(-4 + x)) - 6*(-2 + x) *cos (x*(-4 + x))*sin\sin (x*(-4 + x))/ + 2*(-2 + x) *sin (x*(-4 + x))*sin\sin (x*(-4 + x))/ - 8*(-2 + x) *cos (x*(-4 + x))*sin (x*(-4 + x))*cos\sin (x*(-4 + x))//
8(−8(x−2)2sin⁡4(x(x−4))cos⁡2(x(x−4))cos⁡(sin⁡4(x(x−4)))+2(x−2)2sin⁡2(x(x−4))sin⁡(sin⁡4(x(x−4)))−6(x−2)2sin⁡(sin⁡4(x(x−4)))cos⁡2(x(x−4))−sin⁡(x(x−4))sin⁡(sin⁡4(x(x−4)))cos⁡(x(x−4)))sin⁡2(x(x−4))8 \left(- 8 \left(x - 2\right)^{2} \sin^{4}{\left(x \left(x - 4\right) \right)} \cos^{2}{\left(x \left(x - 4\right) \right)} \cos{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} + 2 \left(x - 2\right)^{2} \sin^{2}{\left(x \left(x - 4\right) \right)} \sin{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} - 6 \left(x - 2\right)^{2} \sin{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} \cos^{2}{\left(x \left(x - 4\right) \right)} - \sin{\left(x \left(x - 4\right) \right)} \sin{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} \cos{\left(x \left(x - 4\right) \right)}\right) \sin^{2}{\left(x \left(x - 4\right) \right)}
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Tercera derivada [src] 
            /     3                /   4            \              2    3                /   4            \         2                5                /   4            \        2                /   4            \                              2    3                4                /   4            \              2    2                                /   4            \              2    6                /   4            \                              2    3                8                /   4            \\                
16*(-2 + x)*\3*sin (x*(-4 + x))*sin\sin (x*(-4 + x))/ - 12*(-2 + x) *cos (x*(-4 + x))*sin\sin (x*(-4 + x))/ - 12*cos (x*(-4 + x))*sin (x*(-4 + x))*cos\sin (x*(-4 + x))/ - 9*cos (x*(-4 + x))*sin\sin (x*(-4 + x))/*sin(x*(-4 + x)) - 72*(-2 + x) *cos (x*(-4 + x))*sin (x*(-4 + x))*cos\sin (x*(-4 + x))/ + 20*(-2 + x) *sin (x*(-4 + x))*cos(x*(-4 + x))*sin\sin (x*(-4 + x))/ + 24*(-2 + x) *sin (x*(-4 + x))*cos\sin (x*(-4 + x))/*cos(x*(-4 + x)) + 32*(-2 + x) *cos (x*(-4 + x))*sin (x*(-4 + x))*sin\sin (x*(-4 + x))//*sin(x*(-4 + x))
16(x−2)(32(x−2)2sin⁡8(x(x−4))sin⁡(sin⁡4(x(x−4)))cos⁡3(x(x−4))+24(x−2)2sin⁡6(x(x−4))cos⁡(x(x−4))cos⁡(sin⁡4(x(x−4)))−72(x−2)2sin⁡4(x(x−4))cos⁡3(x(x−4))cos⁡(sin⁡4(x(x−4)))+20(x−2)2sin⁡2(x(x−4))sin⁡(sin⁡4(x(x−4)))cos⁡(x(x−4))−12(x−2)2sin⁡(sin⁡4(x(x−4)))cos⁡3(x(x−4))−12sin⁡5(x(x−4))cos⁡2(x(x−4))cos⁡(sin⁡4(x(x−4)))+3sin⁡3(x(x−4))sin⁡(sin⁡4(x(x−4)))−9sin⁡(x(x−4))sin⁡(sin⁡4(x(x−4)))cos⁡2(x(x−4)))sin⁡(x(x−4))16 \left(x - 2\right) \left(32 \left(x - 2\right)^{2} \sin^{8}{\left(x \left(x - 4\right) \right)} \sin{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} \cos^{3}{\left(x \left(x - 4\right) \right)} + 24 \left(x - 2\right)^{2} \sin^{6}{\left(x \left(x - 4\right) \right)} \cos{\left(x \left(x - 4\right) \right)} \cos{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} - 72 \left(x - 2\right)^{2} \sin^{4}{\left(x \left(x - 4\right) \right)} \cos^{3}{\left(x \left(x - 4\right) \right)} \cos{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} + 20 \left(x - 2\right)^{2} \sin^{2}{\left(x \left(x - 4\right) \right)} \sin{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} \cos{\left(x \left(x - 4\right) \right)} - 12 \left(x - 2\right)^{2} \sin{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} \cos^{3}{\left(x \left(x - 4\right) \right)} - 12 \sin^{5}{\left(x \left(x - 4\right) \right)} \cos^{2}{\left(x \left(x - 4\right) \right)} \cos{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} + 3 \sin^{3}{\left(x \left(x - 4\right) \right)} \sin{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} - 9 \sin{\left(x \left(x - 4\right) \right)} \sin{\left(\sin^{4}{\left(x \left(x - 4\right) \right)} \right)} \cos^{2}{\left(x \left(x - 4\right) \right)}\right) \sin{\left(x \left(x - 4\right) \right)}
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Gráfico
Derivada de y=cos(sin^4(x^2-4x))
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