Sr Examen

Otras calculadoras

y=lg(x+3)*arctan(5x)^2
Derivada de la función/ (x+3)/ arctan/ y=lg(x+3)*arctan(5x)^2

Derivada de y=lg(x+3)*arctan(5x)^2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
               2     
log(x + 3)*atan (5*x)
log⁡(x+3)atan⁡2(5x)\log{\left(x + 3 \right)} \operatorname{atan}^{2}{\left(5 x \right)} 
log(x + 3)*atan(5*x)^2
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    2                               
atan (5*x)   10*atan(5*x)*log(x + 3)
---------- + -----------------------
  x + 3                     2       
                    1 + 25*x
10log⁡(x+3)atan⁡(5x)25x2+1+atan⁡2(5x)x+3\frac{10 \log{\left(x + 3 \right)} \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}^{2}{\left(5 x \right)}}{x + 3}
Simplificar
Segunda derivada [src] 
      2                                                                 
  atan (5*x)   50*(-1 + 10*x*atan(5*x))*log(3 + x)       20*atan(5*x)   
- ---------- - ----------------------------------- + -------------------
          2                           2              /        2\        
   (3 + x)                 /        2\               \1 + 25*x /*(3 + x)
                           \1 + 25*x /
−50(10xatan⁡(5x)−1)log⁡(x+3)(25x2+1)2+20atan⁡(5x)(x+3)(25x2+1)−atan⁡2(5x)(x+3)2- \frac{50 \left(10 x \operatorname{atan}{\left(5 x \right)} - 1\right) \log{\left(x + 3 \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{20 \operatorname{atan}{\left(5 x \right)}}{\left(x + 3\right) \left(25 x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(5 x \right)}}{\left(x + 3\right)^{2}}
Simplificar
Tercera derivada [src] 
  /                 /                 2                      \                                                             \
  |                 |   15*x     100*x *atan(5*x)            |                                                             |
  |             250*|--------- - ---------------- + atan(5*x)|*log(3 + x)                                                  |
  |    2            |        2              2                |                                                             |
  |atan (5*x)       \1 + 25*x       1 + 25*x                 /              75*(-1 + 10*x*atan(5*x))       15*atan(5*x)    |
2*|---------- - --------------------------------------------------------- - ------------------------ - --------------------|
  |        3                                      2                                      2             /        2\        2|
  | (3 + x)                            /        2\                            /        2\              \1 + 25*x /*(3 + x) |
  \                                    \1 + 25*x /                            \1 + 25*x / *(3 + x)                         /
2(−250(−100x2atan⁡(5x)25x2+1+15x25x2+1+atan⁡(5x))log⁡(x+3)(25x2+1)2−75(10xatan⁡(5x)−1)(x+3)(25x2+1)2−15atan⁡(5x)(x+3)2(25x2+1)+atan⁡2(5x)(x+3)3)2 \left(- \frac{250 \left(- \frac{100 x^{2} \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{15 x}{25 x^{2} + 1} + \operatorname{atan}{\left(5 x \right)}\right) \log{\left(x + 3 \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{75 \left(10 x \operatorname{atan}{\left(5 x \right)} - 1\right)}{\left(x + 3\right) \left(25 x^{2} + 1\right)^{2}} - \frac{15 \operatorname{atan}{\left(5 x \right)}}{\left(x + 3\right)^{2} \left(25 x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(5 x \right)}}{\left(x + 3\right)^{3}}\right)
Simplificar
Gráfico
Derivada de y=lg(x+3)*arctan(5x)^2
    © Sr Examen – Калькулятор