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 1/(x+1)^2
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Derivada de x^12
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Derivada de (x+3)/(x-2)
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Derivada de (x^3-4)
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Expresiones idénticas
- y= uno ÷abtan^- uno (b÷atanx)
- y es igual a 1÷ab tangente de en el grado menos 1(b÷ arco tangente de gente de x)
- y es igual a uno ÷ab tangente de en el grado menos uno (b÷ arco tangente de gente de x)
- y=1÷abtan-1(b÷atanx)
- y=1÷abtan-1b÷atanx
- y=1÷abtan^-1b÷atanx
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Expresiones semejantes
- y=1÷abtan^+1(b÷atanx)
Derivada de y=1÷abtan^-1(b÷atanx)
Solución
Ha introducido
[src]
/b\
|-|
\a/
------------
/ b \
tan|-------|
\atan(x)/
$$\frac{\frac{1}{a} b}{\tan{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)}}$$
(b/a)/tan(b/atan(x))
Primera derivada
[src]
2 / 2/ b \\
b *|1 + tan |-------||
\ \atan(x)//
---------------------------------
/ 2\ 2 2/ b \
a*\1 + x /*atan (x)*tan |-------|
\atan(x)/
$$\frac{b^{2} \left(\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} + 1\right)}{a \left(x^{2} + 1\right) \tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{2}{\left(x \right)}}$$
Segunda derivada
[src]
/ / 2/ b \\ \
| b*|1 + tan |-------|| |
2 / 2/ b \\ | b x 1 \ \atan(x)// |
-2*b *|1 + tan |-------||*|-------- + ------------ + -------------------- - ----------------------|
\ \atan(x)// | 2 / b \ / b \ 2 2/ b \|
|atan (x) tan|-------| atan(x)*tan|-------| atan (x)*tan |-------||
\ \atan(x)/ \atan(x)/ \atan(x)//
---------------------------------------------------------------------------------------------------
2
/ 2\ 2 / b \
a*\1 + x / *atan (x)*tan|-------|
\atan(x)/
$$- \frac{2 b^{2} \left(\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} + 1\right) \left(- \frac{b \left(\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} + 1\right)}{\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{2}{\left(x \right)}} + \frac{b}{\operatorname{atan}^{2}{\left(x \right)}} + \frac{x}{\tan{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)}} + \frac{1}{\tan{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}{\left(x \right)}}\right)}{a \left(x^{2} + 1\right)^{2} \tan{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{2}{\left(x \right)}}$$
Tercera derivada
[src]
/ 2 \
| / 2/ b \\ 2 / 2/ b \\ 2 / 2/ b \\ / 2/ b \\ |
| 2 2 6*b*|1 + tan |-------|| 5*b *|1 + tan |-------|| 3*b *|1 + tan |-------|| 6*b*x*|1 + tan |-------|| |
2 / 2/ b \\ | 1 2*b 3 4*x 6*b 6*x \ \atan(x)// \ \atan(x)// \ \atan(x)// 6*b*x \ \atan(x)// |
2*b *|1 + tan |-------||*|- ------------- + ----------------- + ------------------------------- + ---------------------- + ------------------------------ + ------------------------------ - ------------------------------- - ------------------------------- + ------------------------------- + ------------------------------ - -------------------------------|
\ \atan(x)// | 2/ b \ / 2\ 4 / 2\ 2 2/ b \ / 2\ 2/ b \ / 2\ 3 / b \ / 2\ 2/ b \ / 2\ 3 3/ b \ / 2\ 4 2/ b \ / 2\ 4 4/ b \ / 2\ 2 / b \ / 2\ 2 3/ b \|
| tan |-------| \1 + x /*atan (x) \1 + x /*atan (x)*tan |-------| \1 + x /*tan |-------| \1 + x /*atan (x)*tan|-------| \1 + x /*atan(x)*tan |-------| \1 + x /*atan (x)*tan |-------| \1 + x /*atan (x)*tan |-------| \1 + x /*atan (x)*tan |-------| \1 + x /*atan (x)*tan|-------| \1 + x /*atan (x)*tan |-------||
\ \atan(x)/ \atan(x)/ \atan(x)/ \atan(x)/ \atan(x)/ \atan(x)/ \atan(x)/ \atan(x)/ \atan(x)/ \atan(x)//
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2\ 2
a*\1 + x / *atan (x)
$$\frac{2 b^{2} \left(\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} + 1\right) \left(\frac{3 b^{2} \left(\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} + 1\right)^{2}}{\left(x^{2} + 1\right) \tan^{4}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{4}{\left(x \right)}} - \frac{5 b^{2} \left(\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} + 1\right)}{\left(x^{2} + 1\right) \tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{4}{\left(x \right)}} + \frac{2 b^{2}}{\left(x^{2} + 1\right) \operatorname{atan}^{4}{\left(x \right)}} - \frac{6 b x \left(\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} + 1\right)}{\left(x^{2} + 1\right) \tan^{3}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{2}{\left(x \right)}} + \frac{6 b x}{\left(x^{2} + 1\right) \tan{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{2}{\left(x \right)}} - \frac{6 b \left(\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} + 1\right)}{\left(x^{2} + 1\right) \tan^{3}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{3}{\left(x \right)}} + \frac{6 b}{\left(x^{2} + 1\right) \tan{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{3}{\left(x \right)}} + \frac{4 x^{2}}{\left(x^{2} + 1\right) \tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)}} + \frac{6 x}{\left(x^{2} + 1\right) \tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}{\left(x \right)}} - \frac{1}{\tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)}} + \frac{3}{\left(x^{2} + 1\right) \tan^{2}{\left(\frac{b}{\operatorname{atan}{\left(x \right)}} \right)} \operatorname{atan}^{2}{\left(x \right)}}\right)}{a \left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}}$$