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y=sinxsqrtxarccos(5x+3)
Derivada de la función/ y=sin/ xsqrt/ sqrtx/ arccos/ y=sinxsqrtxarccos(5x+3)

Derivada de y=sinxsqrtxarccos(5x+3)

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

Ha introducido [src] 
         ___              
sin(x)*\/ x *acos(5*x + 3)
xsin⁡(x)acos⁡(5x+3)\sqrt{x} \sin{\left(x \right)} \operatorname{acos}{\left(5 x + 3 \right)} 
(sin(x)*sqrt(x))*acos(5*x + 3)
Gráfica
02468-8-6-4-2-10102-2
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Primera derivada [src] 
                                                ___         
/  ___           sin(x)\                    5*\/ x *sin(x)  
|\/ x *cos(x) + -------|*acos(5*x + 3) - -------------------
|                   ___|                    ________________
\               2*\/ x /                   /              2 
                                         \/  1 - (5*x + 3)
−5xsin⁡(x)1−(5x+3)2+(xcos⁡(x)+sin⁡(x)2x)acos⁡(5x+3)- \frac{5 \sqrt{x} \sin{\left(x \right)}}{\sqrt{1 - \left(5 x + 3\right)^{2}}} + \left(\sqrt{x} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{2 \sqrt{x}}\right) \operatorname{acos}{\left(5 x + 3 \right)}
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Segunda derivada [src] 
 /  /sin(x)       ___       \   /sin(x)   4*cos(x)       ___       \                                          \
 |5*|------ + 2*\/ x *cos(x)|   |------ - -------- + 4*\/ x *sin(x)|*acos(3 + 5*x)                            |
 |  |  ___                  |   |  3/2       ___                   |                      ___                 |
 |  \\/ x                   /   \ x        \/ x                    /                 25*\/ x *(3 + 5*x)*sin(x)|
-|--------------------------- + -------------------------------------------------- + -------------------------|
 |       ________________                               4                                               3/2   |
 |      /              2                                                                /             2\      |
 \    \/  1 - (3 + 5*x)                                                                 \1 - (3 + 5*x) /      /
−(25x(5x+3)sin⁡(x)(1−(5x+3)2)32+(4xsin⁡(x)−4cos⁡(x)x+sin⁡(x)x32)acos⁡(5x+3)4+5(2xcos⁡(x)+sin⁡(x)x)1−(5x+3)2)- (\frac{25 \sqrt{x} \left(5 x + 3\right) \sin{\left(x \right)}}{\left(1 - \left(5 x + 3\right)^{2}\right)^{\frac{3}{2}}} + \frac{\left(4 \sqrt{x} \sin{\left(x \right)} - \frac{4 \cos{\left(x \right)}}{\sqrt{x}} + \frac{\sin{\left(x \right)}}{x^{\frac{3}{2}}}\right) \operatorname{acos}{\left(5 x + 3 \right)}}{4} + \frac{5 \left(2 \sqrt{x} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{\sqrt{x}}\right)}{\sqrt{1 - \left(5 x + 3\right)^{2}}})
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Tercera derivada [src] 
                                                                                                                                                                    /                  2 \       
  /  3*sin(x)   6*cos(x)       ___          12*sin(x)\                    /sin(x)   4*cos(x)       ___       \                /sin(x)       ___       \         ___ |       3*(3 + 5*x)  |       
  |- -------- + -------- + 8*\/ x *cos(x) + ---------|*acos(3 + 5*x)   15*|------ - -------- + 4*\/ x *sin(x)|   75*(3 + 5*x)*|------ + 2*\/ x *cos(x)|   125*\/ x *|-1 + ---------------|*sin(x)
  |     5/2        3/2                          ___  |                    |  3/2       ___                   |                |  ___                  |             |                   2|       
  \    x          x                           \/ x   /                    \ x        \/ x                    /                \\/ x                   /             \     -1 + (3 + 5*x) /       
- ------------------------------------------------------------------ + --------------------------------------- - -------------------------------------- + ---------------------------------------
                                  8                                                  ________________                                      3/2                                      3/2          
                                                                                    /              2                       /             2\                         /             2\             
                                                                                4*\/  1 - (3 + 5*x)                      2*\1 - (3 + 5*x) /                         \1 - (3 + 5*x) /
125x(3(5x+3)2(5x+3)2−1−1)sin⁡(x)(1−(5x+3)2)32−(8xcos⁡(x)+12sin⁡(x)x+6cos⁡(x)x32−3sin⁡(x)x52)acos⁡(5x+3)8+15(4xsin⁡(x)−4cos⁡(x)x+sin⁡(x)x32)41−(5x+3)2−75(5x+3)(2xcos⁡(x)+sin⁡(x)x)2(1−(5x+3)2)32\frac{125 \sqrt{x} \left(\frac{3 \left(5 x + 3\right)^{2}}{\left(5 x + 3\right)^{2} - 1} - 1\right) \sin{\left(x \right)}}{\left(1 - \left(5 x + 3\right)^{2}\right)^{\frac{3}{2}}} - \frac{\left(8 \sqrt{x} \cos{\left(x \right)} + \frac{12 \sin{\left(x \right)}}{\sqrt{x}} + \frac{6 \cos{\left(x \right)}}{x^{\frac{3}{2}}} - \frac{3 \sin{\left(x \right)}}{x^{\frac{5}{2}}}\right) \operatorname{acos}{\left(5 x + 3 \right)}}{8} + \frac{15 \left(4 \sqrt{x} \sin{\left(x \right)} - \frac{4 \cos{\left(x \right)}}{\sqrt{x}} + \frac{\sin{\left(x \right)}}{x^{\frac{3}{2}}}\right)}{4 \sqrt{1 - \left(5 x + 3\right)^{2}}} - \frac{75 \left(5 x + 3\right) \left(2 \sqrt{x} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{\sqrt{x}}\right)}{2 \left(1 - \left(5 x + 3\right)^{2}\right)^{\frac{3}{2}}}
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Gráfico
Derivada de y=sinxsqrtxarccos(5x+3)
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