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
-
¿Cómo usar?
- Derivada de:
-
Derivada de 2*cos(3*x)
-
Derivada de x^(7/6)
-
Derivada de x^(2/5)
-
Derivada de 1/ln(x)
- Integral de d{x}:
- √x/(√x+1)
-
Expresiones idénticas
- √x/(√x+ uno)
- √x dividir por (√x más 1)
- √x dividir por (√x más uno)
- √x/√x+1
- √x dividir por (√x+1)
-
Expresiones semejantes
- √x/(√x-1)
- (√x)/((√x)+1)
- √(x)/√(x+1)
- ((√x))/(√x)+1
- ((√x))/((√x)+1)
- y=√x/√x+1
Derivada de √x/(√x+1)
Solución
Ha introducido
[src]
___ \/ x --------- ___ \/ x + 1
$$\frac{\sqrt{x}}{\sqrt{x} + 1}$$
sqrt(x)/(sqrt(x) + 1)
Solución detallada
-
Se aplica la regla de la derivada parcial:
y .
Para calcular :
-
Según el principio, aplicamos: tenemos
Para calcular :
-
diferenciamos miembro por miembro:
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La derivada de una constante es igual a cero.
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Según el principio, aplicamos: tenemos
Como resultado de:
-
Ahora aplicamos la regla de la derivada de una divesión:
-
-
Simplificamos:
Respuesta:
Primera derivada
[src]
1 1
- -------------- + -------------------
2 ___ / ___ \
/ ___ \ 2*\/ x *\\/ x + 1/
2*\\/ x + 1/
$$- \frac{1}{2 \left(\sqrt{x} + 1\right)^{2}} + \frac{1}{2 \sqrt{x} \left(\sqrt{x} + 1\right)}$$
Segunda derivada
[src]
___ / 1 2 \
\/ x *|---- + -------------|
| 3/2 / ___\|
1 2 \x x*\1 + \/ x //
- ---- - ------------- + ----------------------------
3/2 / ___\ ___
x x*\1 + \/ x / 1 + \/ x
-----------------------------------------------------
/ ___\
4*\1 + \/ x /
$$\frac{\frac{\sqrt{x} \left(\frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{\sqrt{x} + 1} - \frac{2}{x \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}}{4 \left(\sqrt{x} + 1\right)}$$
Tercera derivada
[src]
/ ___ / 1 2 2 \\
| 1 2 \/ x *|---- + -------------- + -----------------||
| ---- + ------------- | 5/2 2 / ___\ 2||
| 3/2 / ___\ |x x *\1 + \/ x / 3/2 / ___\ ||
| 1 1 x x*\1 + \/ x / \ x *\1 + \/ x / /|
3*|---- + -------------- + -------------------- - -------------------------------------------------|
| 5/2 2 / ___\ ___ / ___\ ___ |
\x x *\1 + \/ x / \/ x *\1 + \/ x / 1 + \/ x /
----------------------------------------------------------------------------------------------------
/ ___\
8*\1 + \/ x /
$$\frac{3 \left(- \frac{\sqrt{x} \left(\frac{2}{x^{2} \left(\sqrt{x} + 1\right)} + \frac{2}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{1}{x^{\frac{5}{2}}}\right)}{\sqrt{x} + 1} + \frac{1}{x^{2} \left(\sqrt{x} + 1\right)} + \frac{\frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{1}{x^{\frac{3}{2}}}}{\sqrt{x} \left(\sqrt{x} + 1\right)} + \frac{1}{x^{\frac{5}{2}}}\right)}{8 \left(\sqrt{x} + 1\right)}$$
9-я производная
[src]
/ 429 128 448 858 864 1188 1200 1320 ___ / 715 128 512 1120 1430 1760 2002 2200 2288 \ / 21 16 40 42 56 56 \ / 33 16 48 66 80 90 96 \ / 7 8 14 16 18 \ / 5 8 10 12 \ / 1 2 2 \ \
| ----- + --------------- + ----------------- + -------------- + --------------- + ------------------ + ------------------ + --------------- \/ x *|----- + ----------------- + --------------- + ------------------ + -------------- + --------------- + ------------------ + ------------------ + ---------------| 4*|----- + --------------- + ----------------- + -------------- + --------------- + -----------------| 4*|----- + ----------------- + --------------- + -------------- + ----------------- + ------------------ + ---------------| 10*|---- + ----------------- + -------------- + --------------- + -----------------| 14*|---- + --------------- + -------------- + -----------------| 84*|---- + -------------- + -----------------| / 1 2 \|
| 15/2 7 6 7 / ___\ 5 2 4 3 | 17/2 8 7 6 8 / ___\ 5 2 4 3| | 11/2 5 4 5 / ___\ 3 2| | 13/2 6 5 6 / ___\ 4 2 3| | 9/2 4 4 / ___\ 3 2| | 7/2 3 3 / ___\ 2| | 5/2 2 / ___\ 2| 132*|---- + -------------||
| x 4 / ___\ 9/2 / ___\ x *\1 + \/ x / 5 / ___\ 13/2 / ___\ 11/2 / ___\ 6 / ___\ |x 9/2 / ___\ 5 / ___\ 11/2 / ___\ x *\1 + \/ x / 6 / ___\ 15/2 / ___\ 13/2 / ___\ 7 / ___\ | |x 3 / ___\ 7/2 / ___\ x *\1 + \/ x / 4 / ___\ 9/2 / ___\ | |x 7/2 / ___\ 4 / ___\ x *\1 + \/ x / 9/2 / ___\ 11/2 / ___\ 5 / ___\ | |x 5/2 / ___\ x *\1 + \/ x / 3 / ___\ 7/2 / ___\ | |x 2 / ___\ x *\1 + \/ x / 5/2 / ___\ | |x x *\1 + \/ x / 3/2 / ___\ | | 3/2 / ___\||
| 715 429 x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / \ x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / / \ x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / / \ x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / / \ x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / / \ x *\1 + \/ x / x *\1 + \/ x / / \ x *\1 + \/ x / / \x x*\1 + \/ x //|
2835*|----- + -------------- + ------------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------ + ---------------------------------------------------------------- + ---------------------------------------------- + --------------------------|
| 17/2 8 / ___\ ___ / ___\ ___ 5/2 / ___\ 3/2 / ___\ 7/2 / ___\ 9/2 / ___\ 11/2 / ___\ 13/2 / ___\ |
\x x *\1 + \/ x / \/ x *\1 + \/ x / 1 + \/ x x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ___\
512*\1 + \/ x /
$$\frac{2835 \left(- \frac{\sqrt{x} \left(\frac{512}{x^{5} \left(\sqrt{x} + 1\right)^{7}} + \frac{1760}{x^{6} \left(\sqrt{x} + 1\right)^{5}} + \frac{2288}{x^{7} \left(\sqrt{x} + 1\right)^{3}} + \frac{1430}{x^{8} \left(\sqrt{x} + 1\right)} + \frac{128}{x^{\frac{9}{2}} \left(\sqrt{x} + 1\right)^{8}} + \frac{1120}{x^{\frac{11}{2}} \left(\sqrt{x} + 1\right)^{6}} + \frac{2200}{x^{\frac{13}{2}} \left(\sqrt{x} + 1\right)^{4}} + \frac{2002}{x^{\frac{15}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{715}{x^{\frac{17}{2}}}\right)}{\sqrt{x} + 1} + \frac{429}{x^{8} \left(\sqrt{x} + 1\right)} + \frac{\frac{128}{x^{4} \left(\sqrt{x} + 1\right)^{7}} + \frac{864}{x^{5} \left(\sqrt{x} + 1\right)^{5}} + \frac{1320}{x^{6} \left(\sqrt{x} + 1\right)^{3}} + \frac{858}{x^{7} \left(\sqrt{x} + 1\right)} + \frac{448}{x^{\frac{9}{2}} \left(\sqrt{x} + 1\right)^{6}} + \frac{1200}{x^{\frac{11}{2}} \left(\sqrt{x} + 1\right)^{4}} + \frac{1188}{x^{\frac{13}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{429}{x^{\frac{15}{2}}}}{\sqrt{x} \left(\sqrt{x} + 1\right)} + \frac{4 \left(\frac{48}{x^{4} \left(\sqrt{x} + 1\right)^{5}} + \frac{96}{x^{5} \left(\sqrt{x} + 1\right)^{3}} + \frac{66}{x^{6} \left(\sqrt{x} + 1\right)} + \frac{16}{x^{\frac{7}{2}} \left(\sqrt{x} + 1\right)^{6}} + \frac{80}{x^{\frac{9}{2}} \left(\sqrt{x} + 1\right)^{4}} + \frac{90}{x^{\frac{11}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{33}{x^{\frac{13}{2}}}\right)}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} + \frac{4 \left(\frac{16}{x^{3} \left(\sqrt{x} + 1\right)^{5}} + \frac{56}{x^{4} \left(\sqrt{x} + 1\right)^{3}} + \frac{42}{x^{5} \left(\sqrt{x} + 1\right)} + \frac{40}{x^{\frac{7}{2}} \left(\sqrt{x} + 1\right)^{4}} + \frac{56}{x^{\frac{9}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{21}{x^{\frac{11}{2}}}\right)}{x^{\frac{5}{2}} \left(\sqrt{x} + 1\right)} + \frac{10 \left(\frac{16}{x^{3} \left(\sqrt{x} + 1\right)^{3}} + \frac{14}{x^{4} \left(\sqrt{x} + 1\right)} + \frac{8}{x^{\frac{5}{2}} \left(\sqrt{x} + 1\right)^{4}} + \frac{18}{x^{\frac{7}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{7}{x^{\frac{9}{2}}}\right)}{x^{\frac{7}{2}} \left(\sqrt{x} + 1\right)} + \frac{14 \left(\frac{8}{x^{2} \left(\sqrt{x} + 1\right)^{3}} + \frac{10}{x^{3} \left(\sqrt{x} + 1\right)} + \frac{12}{x^{\frac{5}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{5}{x^{\frac{7}{2}}}\right)}{x^{\frac{9}{2}} \left(\sqrt{x} + 1\right)} + \frac{84 \left(\frac{2}{x^{2} \left(\sqrt{x} + 1\right)} + \frac{2}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{1}{x^{\frac{5}{2}}}\right)}{x^{\frac{11}{2}} \left(\sqrt{x} + 1\right)} + \frac{132 \left(\frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{x^{\frac{13}{2}} \left(\sqrt{x} + 1\right)} + \frac{715}{x^{\frac{17}{2}}}\right)}{512 \left(\sqrt{x} + 1\right)}$$
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