Sr Examen

Otras calculadoras

y=3^(2*x)*atan(5*x)
Derivada de la función/ 3^(2*x)/ tan(5*x)/ y=3^(2*x)*atan(5*x)

Derivada de y=3^(2*x)*atan(5*x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 2*x          
3   *atan(5*x)
32xatan⁡(5x)3^{2 x} \operatorname{atan}{\left(5 x \right)} 
3^(2*x)*atan(5*x)
Gráfica
02468-8-6-4-2-101020000000000-10000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
     2*x                           
  5*3          2*x                 
--------- + 2*3   *atan(5*x)*log(3)
        2                          
1 + 25*x
2⋅32xlog⁡(3)atan⁡(5x)+5⋅32x25x2+12 \cdot 3^{2 x} \log{\left(3 \right)} \operatorname{atan}{\left(5 x \right)} + \frac{5 \cdot 3^{2 x}}{25 x^{2} + 1}
Simplificar
Segunda derivada [src] 
   2*x /     125*x            2                10*log(3)\
2*3   *|- ------------ + 2*log (3)*atan(5*x) + ---------|
       |             2                                 2|
       |  /        2\                          1 + 25*x |
       \  \1 + 25*x /                                   /
2⋅32x(−125x(25x2+1)2+2log⁡(3)2atan⁡(5x)+10log⁡(3)25x2+1)2 \cdot 3^{2 x} \left(- \frac{125 x}{\left(25 x^{2} + 1\right)^{2}} + 2 \log{\left(3 \right)}^{2} \operatorname{atan}{\left(5 x \right)} + \frac{10 \log{\left(3 \right)}}{25 x^{2} + 1}\right)
Simplificar
Tercera derivada [src] 
       /                                       /            2 \               \
       |                                       |       100*x  |               |
       |                                   125*|-1 + ---------|               |
       |                            2          |             2|               |
   2*x |     3                30*log (3)       \     1 + 25*x /   750*x*log(3)|
2*3   *|4*log (3)*atan(5*x) + ---------- + -------------------- - ------------|
       |                              2                   2                  2|
       |                      1 + 25*x         /        2\        /        2\ |
       \                                       \1 + 25*x /        \1 + 25*x / /
2⋅32x(−750xlog⁡(3)(25x2+1)2+4log⁡(3)3atan⁡(5x)+30log⁡(3)225x2+1+125(100x225x2+1−1)(25x2+1)2)2 \cdot 3^{2 x} \left(- \frac{750 x \log{\left(3 \right)}}{\left(25 x^{2} + 1\right)^{2}} + 4 \log{\left(3 \right)}^{3} \operatorname{atan}{\left(5 x \right)} + \frac{30 \log{\left(3 \right)}^{2}}{25 x^{2} + 1} + \frac{125 \left(\frac{100 x^{2}}{25 x^{2} + 1} - 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right)
Simplificar
Gráfico
Derivada de y=3^(2*x)*atan(5*x)
    © Sr Examen – Калькулятор