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y=(ln(x-4)^3)+arcsin(2x)^4

Derivada de y=(ln(x-4)^3)+arcsin(2x)^4

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Solución

Ha introducido [src]
   3              4     
log (x - 4) + asin (2*x)
$$\log{\left(x - 4 \right)}^{3} + \operatorname{asin}^{4}{\left(2 x \right)}$$
log(x - 4)^3 + asin(2*x)^4
Gráfica
Primera derivada [src]
     2                 3     
3*log (x - 4)    8*asin (2*x)
------------- + -------------
    x - 4          __________
                  /        2 
                \/  1 - 4*x  
$$\frac{3 \log{\left(x - 4 \right)}^{2}}{x - 4} + \frac{8 \operatorname{asin}^{3}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$
Segunda derivada [src]
         2             2                                    3     
  48*asin (2*x)   3*log (-4 + x)   6*log(-4 + x)   32*x*asin (2*x)
- ------------- - -------------- + ------------- + ---------------
            2               2                2                3/2 
    -1 + 4*x        (-4 + x)         (-4 + x)       /       2\    
                                                    \1 - 4*x /    
$$\frac{32 x \operatorname{asin}^{3}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{48 \operatorname{asin}^{2}{\left(2 x \right)}}{4 x^{2} - 1} - \frac{3 \log{\left(x - 4 \right)}^{2}}{\left(x - 4\right)^{2}} + \frac{6 \log{\left(x - 4 \right)}}{\left(x - 4\right)^{2}}$$
Tercera derivada [src]
  /                                 2                  3                             2     3                  2     \
  |    3       9*log(-4 + x)   3*log (-4 + x)   16*asin (2*x)    96*asin(2*x)   192*x *asin (2*x)   288*x*asin (2*x)|
2*|--------- - ------------- + -------------- + ------------- + ------------- + ----------------- + ----------------|
  |        3             3               3                3/2             3/2               5/2                  2  |
  |(-4 + x)      (-4 + x)        (-4 + x)       /       2\      /       2\        /       2\          /        2\   |
  \                                             \1 - 4*x /      \1 - 4*x /        \1 - 4*x /          \-1 + 4*x /   /
$$2 \left(\frac{192 x^{2} \operatorname{asin}^{3}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{288 x \operatorname{asin}^{2}{\left(2 x \right)}}{\left(4 x^{2} - 1\right)^{2}} + \frac{3 \log{\left(x - 4 \right)}^{2}}{\left(x - 4\right)^{3}} - \frac{9 \log{\left(x - 4 \right)}}{\left(x - 4\right)^{3}} + \frac{3}{\left(x - 4\right)^{3}} + \frac{16 \operatorname{asin}^{3}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{96 \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)$$
Gráfico
Derivada de y=(ln(x-4)^3)+arcsin(2x)^4