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Derivada de la función/ sin^4/ y=sin/ y=sin^45x+cos^45x

Derivada de y=sin^45x+cos^45x

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

Ha introducido [src] 
   45         45   
sin  (x) + cos  (x)
sin⁡45(x)+cos⁡45(x)\sin^{45}{\left(x \right)} + \cos^{45}{\left(x \right)} 
sin(x)^45 + cos(x)^45
Primera derivada [src] 
        44                   44          
- 45*cos  (x)*sin(x) + 45*sin  (x)*cos(x)
45sin⁡44(x)cos⁡(x)−45sin⁡(x)cos⁡44(x)45 \sin^{44}{\left(x \right)} \cos{\left(x \right)} - 45 \sin{\left(x \right)} \cos^{44}{\left(x \right)}
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Segunda derivada [src] 
   /     45         45            2       43            43       2   \
45*\- cos  (x) - sin  (x) + 44*cos (x)*sin  (x) + 44*cos  (x)*sin (x)/
45(−sin⁡45(x)+44sin⁡43(x)cos⁡2(x)+44sin⁡2(x)cos⁡43(x)−cos⁡45(x))45 \left(- \sin^{45}{\left(x \right)} + 44 \sin^{43}{\left(x \right)} \cos^{2}{\left(x \right)} + 44 \sin^{2}{\left(x \right)} \cos^{43}{\left(x \right)} - \cos^{45}{\left(x \right)}\right)
Simplificar
Tercera derivada [src] 
   /         43             43              41       2              2       41   \              
45*\- 133*sin  (x) + 133*cos  (x) - 1892*cos  (x)*sin (x) + 1892*cos (x)*sin  (x)/*cos(x)*sin(x)
45(−133sin⁡43(x)+1892sin⁡41(x)cos⁡2(x)−1892sin⁡2(x)cos⁡41(x)+133cos⁡43(x))sin⁡(x)cos⁡(x)45 \left(- 133 \sin^{43}{\left(x \right)} + 1892 \sin^{41}{\left(x \right)} \cos^{2}{\left(x \right)} - 1892 \sin^{2}{\left(x \right)} \cos^{41}{\left(x \right)} + 133 \cos^{43}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}
Simplificar
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