Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de sin(2*x+3)
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Derivada de 1/sqrtx
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Derivada de 4/x^4
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Derivada de 10+15*x
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Expresiones idénticas
- y=tg(sqrtx)*arctg3x^ cinco
- y es igual a tg( raíz cuadrada de x) multiplicar por arctg3x en el grado 5
- y es igual a tg( raíz cuadrada de x) multiplicar por arctg3x en el grado cinco
- y=tg(√x)*arctg3x^5
- y=tg(sqrtx)*arctg3x5
- y=tgsqrtx*arctg3x5
- y=tg(sqrtx)*arctg3x⁵
- y=tg(sqrtx)arctg3x^5
- y=tg(sqrtx)arctg3x5
- y=tgsqrtxarctg3x5
- y=tgsqrtxarctg3x^5
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Expresiones con funciones
- tg
- tg(x)/x^2
- tg(cosx)
Derivada de y=tg(sqrtx)*arctg3x^5
Solución
Ha introducido
[src]
/ ___\ 5 tan\\/ x /*atan (3*x)
$$\tan{\left(\sqrt{x} \right)} \operatorname{atan}^{5}{\left(3 x \right)}$$
tan(sqrt(x))*atan(3*x)^5
Primera derivada
[src]
5 / 2/ ___\\ 4 / ___\
atan (3*x)*\1 + tan \\/ x // 15*atan (3*x)*tan\\/ x /
---------------------------- + ------------------------
___ 2
2*\/ x 1 + 9*x
$$\frac{15 \tan{\left(\sqrt{x} \right)} \operatorname{atan}^{4}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{5}{\left(3 x \right)}}{2 \sqrt{x}}$$
Segunda derivada
[src]
/ / / ___\\ \
| 2 / 2/ ___\\ | 1 2*tan\\/ x /| |
| atan (3*x)*\1 + tan \\/ x //*|- ---- + ------------| |
| / ___\ | 3/2 x | / 2/ ___\\ |
3 | 90*(-2 + 3*x*atan(3*x))*tan\\/ x / \ x / 15*\1 + tan \\/ x //*atan(3*x)|
atan (3*x)*|- ---------------------------------- + ---------------------------------------------------- + ------------------------------|
| 2 4 ___ / 2\ |
| / 2\ \/ x *\1 + 9*x / |
\ \1 + 9*x / /
$$\left(\frac{\left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}{4} - \frac{90 \left(3 x \operatorname{atan}{\left(3 x \right)} - 2\right) \tan{\left(\sqrt{x} \right)}}{\left(9 x^{2} + 1\right)^{2}} + \frac{15 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}{\left(3 x \right)}}{\sqrt{x} \left(9 x^{2} + 1\right)}\right) \operatorname{atan}^{3}{\left(3 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ / / ___\ / 2/ ___\\ 2/ ___\\ / / ___\\ \
| | 2 6 36*x*atan(3*x) 36*x *atan (3*x)| / ___\ 3 / 2/ ___\\ | 3 6*tan\\/ x / 2*\1 + tan \\/ x // 4*tan \\/ x /| 2 / 2/ ___\\ | 1 2*tan\\/ x /| |
|270*|- atan (3*x) + -------- - -------------- + ----------------|*tan\\/ x / atan (3*x)*\1 + tan \\/ x //*|---- - ------------ + ------------------- + -------------| 45*atan (3*x)*\1 + tan \\/ x //*|- ---- + ------------| |
| | 2 2 2 | | 5/2 2 3/2 3/2 | | 3/2 x | / 2/ ___\\ |
2 | \ 1 + 9*x 1 + 9*x 1 + 9*x / \x x x x / \ x / 135*\1 + tan \\/ x //*(-2 + 3*x*atan(3*x))*atan(3*x)|
atan (3*x)*|---------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- + ------------------------------------------------------- - ----------------------------------------------------|
| 2 8 / 2\ 2 |
| / 2\ 4*\1 + 9*x / ___ / 2\ |
\ \1 + 9*x / \/ x *\1 + 9*x / /
$$\left(\frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \left(- \frac{6 \tan{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{x^{\frac{3}{2}}} + \frac{4 \tan^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}}}\right) \operatorname{atan}^{3}{\left(3 x \right)}}{8} + \frac{45 \left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}{4 \left(9 x^{2} + 1\right)} + \frac{270 \left(\frac{36 x^{2} \operatorname{atan}^{2}{\left(3 x \right)}}{9 x^{2} + 1} - \frac{36 x \operatorname{atan}{\left(3 x \right)}}{9 x^{2} + 1} - \operatorname{atan}^{2}{\left(3 x \right)} + \frac{6}{9 x^{2} + 1}\right) \tan{\left(\sqrt{x} \right)}}{\left(9 x^{2} + 1\right)^{2}} - \frac{135 \left(3 x \operatorname{atan}{\left(3 x \right)} - 2\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}{\left(3 x \right)}}{\sqrt{x} \left(9 x^{2} + 1\right)^{2}}\right) \operatorname{atan}^{2}{\left(3 x \right)}$$
Gráfico