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y=(1-5x)^4+sin(x)^2-cos(sqrt(x))+(sqrt(3x)-1)/(1-5x)+pi^3
Derivada de la función/ y=(1-5x)^4+sin(x)^2-cos(sqrt(x))+(sqrt(3x)-1)/(1-5x)+pi^3

Derivada de y=(1-5x)^4+sin(x)^2-cos(sqrt(x))+(sqrt(3x)-1)/(1-5x)+pi^3

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

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Solución

Ha introducido [src] 
                                      _____          
         4      2         /  ___\   \/ 3*x  - 1     3
(1 - 5*x)  + sin (x) - cos\\/ x / + ----------- + pi 
                                      1 - 5*x
((((1−5x)4+sin⁡2(x))−cos⁡(x))+3x−11−5x)+π3\left(\left(\left(\left(1 - 5 x\right)^{4} + \sin^{2}{\left(x \right)}\right) - \cos{\left(\sqrt{x} \right)}\right) + \frac{\sqrt{3 x} - 1}{1 - 5 x}\right) + \pi^{3} 
(1 - 5*x)^4 + sin(x)^2 - cos(sqrt(x)) + (sqrt(3*x) - 1)/(1 - 5*x) + pi^3
Gráfica
02468-8-6-4-2-1010-1000000010000000
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Primera derivada [src] 
                     /  ___\                       /  _____    \           ___      
              3   sin\\/ x /                     5*\\/ 3*x  - 1/         \/ 3       
- 20*(1 - 5*x)  + ---------- + 2*cos(x)*sin(x) + --------------- + -----------------
                       ___                                   2         ___          
                   2*\/ x                           (1 - 5*x)      2*\/ x *(1 - 5*x)
−20(1−5x)3+2sin⁡(x)cos⁡(x)+5(3x−1)(1−5x)2+sin⁡(x)2x+32x(1−5x)- 20 \left(1 - 5 x\right)^{3} + 2 \sin{\left(x \right)} \cos{\left(x \right)} + \frac{5 \left(\sqrt{3 x} - 1\right)}{\left(1 - 5 x\right)^{2}} + \frac{\sin{\left(\sqrt{x} \right)}}{2 \sqrt{x}} + \frac{\sqrt{3}}{2 \sqrt{x} \left(1 - 5 x\right)}
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Segunda derivada [src] 
                                               /       ___   ___\      /  ___\      /  ___\            ___                ___      
       2           2                    2   50*\-1 + \/ 3 *\/ x /   sin\\/ x /   cos\\/ x /        5*\/ 3               \/ 3       
- 2*sin (x) + 2*cos (x) + 300*(-1 + 5*x)  - --------------------- - ---------- + ---------- + ----------------- + -----------------
                                                           3             3/2        4*x         ___           2      3/2           
                                                 (-1 + 5*x)           4*x                     \/ x *(-1 + 5*x)    4*x   *(-1 + 5*x)
300(5x−1)2−2sin⁡2(x)+2cos⁡2(x)−50(3x−1)(5x−1)3+cos⁡(x)4x+53x(5x−1)2−sin⁡(x)4x32+34x32(5x−1)300 \left(5 x - 1\right)^{2} - 2 \sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)} - \frac{50 \left(\sqrt{3} \sqrt{x} - 1\right)}{\left(5 x - 1\right)^{3}} + \frac{\cos{\left(\sqrt{x} \right)}}{4 x} + \frac{5 \sqrt{3}}{\sqrt{x} \left(5 x - 1\right)^{2}} - \frac{\sin{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}}} + \frac{\sqrt{3}}{4 x^{\frac{3}{2}} \left(5 x - 1\right)}
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Tercera derivada [src] 
                                        /       ___   ___\        /  ___\      /  ___\        /  ___\             ___                 ___                 ___     
                                    750*\-1 + \/ 3 *\/ x /   3*cos\\/ x /   sin\\/ x /   3*sin\\/ x /        75*\/ 3             15*\/ 3              3*\/ 3      
-3000 + 15000*x - 8*cos(x)*sin(x) + ---------------------- - ------------ - ---------- + ------------ - ----------------- - ------------------ - -----------------
                                                   4                2            3/2           5/2        ___           3      3/2           2      5/2           
                                         (-1 + 5*x)              8*x          8*x           8*x         \/ x *(-1 + 5*x)    4*x   *(-1 + 5*x)    8*x   *(-1 + 5*x)
15000x−8sin⁡(x)cos⁡(x)−3000+750(3x−1)(5x−1)4−3cos⁡(x)8x2−753x(5x−1)3−sin⁡(x)8x32−1534x32(5x−1)2+3sin⁡(x)8x52−338x52(5x−1)15000 x - 8 \sin{\left(x \right)} \cos{\left(x \right)} - 3000 + \frac{750 \left(\sqrt{3} \sqrt{x} - 1\right)}{\left(5 x - 1\right)^{4}} - \frac{3 \cos{\left(\sqrt{x} \right)}}{8 x^{2}} - \frac{75 \sqrt{3}}{\sqrt{x} \left(5 x - 1\right)^{3}} - \frac{\sin{\left(\sqrt{x} \right)}}{8 x^{\frac{3}{2}}} - \frac{15 \sqrt{3}}{4 x^{\frac{3}{2}} \left(5 x - 1\right)^{2}} + \frac{3 \sin{\left(\sqrt{x} \right)}}{8 x^{\frac{5}{2}}} - \frac{3 \sqrt{3}}{8 x^{\frac{5}{2}} \left(5 x - 1\right)}
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Gráfico
Derivada de y=(1-5x)^4+sin(x)^2-cos(sqrt(x))+(sqrt(3x)-1)/(1-5x)+pi^3
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