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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- Derivada de:
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Derivada de x^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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Expresiones idénticas
- x*exp(-x)sqrt((quince -x)*(x- diez))-arctg(sqrt((quince -x)/(x- diez)))
- x multiplicar por exponente de ( menos x) raíz cuadrada de ((15 menos x) multiplicar por (x menos 10)) menos arctg( raíz cuadrada de ((15 menos x) dividir por (x menos 10)))
- x multiplicar por exponente de ( menos x) raíz cuadrada de ((quince menos x) multiplicar por (x menos diez)) menos arctg( raíz cuadrada de ((quince menos x) dividir por (x menos diez)))
- x*exp(-x)√((15-x)*(x-10))-arctg(√((15-x)/(x-10)))
- xexp(-x)sqrt((15-x)(x-10))-arctg(sqrt((15-x)/(x-10)))
- xexp-xsqrt15-xx-10-arctgsqrt15-x/x-10
- x*exp(-x)sqrt((15-x)*(x-10))-arctg(sqrt((15-x) dividir por (x-10)))
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Expresiones semejantes
- x*exp(-x)sqrt((15-x)*(x-10))+arctg(sqrt((15-x)/(x-10)))
- x*exp(x)sqrt((15-x)*(x-10))-arctg(sqrt((15-x)/(x-10)))
- x*exp(-x)sqrt((15-x)*(x-10))-arctg(sqrt((15-x)/(x+10)))
- x*exp(-x)sqrt((15-x)*(x+10))-arctg(sqrt((15-x)/(x-10)))
- x*exp(-x)sqrt((15+x)*(x-10))-arctg(sqrt((15-x)/(x-10)))
- x*exp(-x)sqrt((15-x)*(x-10))-arctg(sqrt((15+x)/(x-10)))
Derivada de x*exp(-x)sqrt((15-x)*(x-10))-arctg(sqrt((15-x)/(x-10)))
Solución
Ha introducido
[src]
/ ________\
-x ___________________ | / 15 - x |
x*e *\/ (15 - x)*(x - 10) - atan| / ------ |
\\/ x - 10 /
$$x e^{- x} \sqrt{\left(15 - x\right) \left(x - 10\right)} - \operatorname{atan}{\left(\sqrt{\frac{15 - x}{x - 10}} \right)}$$
(x*exp(-x))*sqrt((15 - x)*(x - 10)) - atan(sqrt((15 - x)/(x - 10)))
Primera derivada
[src]
________
/ 15 - x / 1 15 - x \
/ ------ *(x - 10)*|- ---------- - -----------|
\/ x - 10 | 2*(x - 10) 2| ___________________ -x
___________________ / -x -x\ \ 2*(x - 10) / x*\/ (15 - x)*(x - 10) *(25/2 - x)*e
\/ (15 - x)*(x - 10) *\- x*e + e / - -------------------------------------------------- + --------------------------------------
/ 15 - x\ (15 - x)*(x - 10)
|1 + ------|*(15 - x)
\ x - 10/
$$\frac{x \sqrt{\left(15 - x\right) \left(x - 10\right)} \left(\frac{25}{2} - x\right) e^{- x}}{\left(15 - x\right) \left(x - 10\right)} - \frac{\sqrt{\frac{15 - x}{x - 10}} \left(x - 10\right) \left(- \frac{15 - x}{2 \left(x - 10\right)^{2}} - \frac{1}{2 \left(x - 10\right)}\right)}{\left(15 - x\right) \left(\frac{15 - x}{x - 10} + 1\right)} + \sqrt{\left(15 - x\right) \left(x - 10\right)} \left(- x e^{- x} + e^{- x}\right)$$
Segunda derivada
[src]
_____________ _____________
/ -(-15 + x) / -(-15 + x) / -15 + x\
/ ----------- / ----------- *|-1 + -------| ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ 2 -x
\/ -10 + x ______________________ -x \/ -10 + x \ -10 + x/ x*\/ -(-15 + x)*(-10 + x) *e \/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e \/ -(-15 + x)*(-10 + x) *(-1 + x)*(-25 + 2*x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x) *e
----------------- + \/ -(-15 + x)*(-10 + x) *(-2 + x)*e + -------------------------------- + ------------------------------ + ---------------------------------------- - ------------------------------------------ - ------------------------------------------ - ------------------------------------------ - ------------------------------------------------- + -------------------------------------------
2 2 (-15 + x)*(-10 + x) 2*(-15 + x)*(-10 + x) 2*(-15 + x)*(-10 + x) 2 2 2*(-15 + x)*(-10 + x) 2 2
2*(-15 + x) 4*(-15 + x) 2*(-15 + x)*(-10 + x) 2*(-15 + x) *(-10 + x) 4*(-15 + x) *(-10 + x)
$$- \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right) \left(x - 10\right)} + \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} e^{- x}}{\left(x - 15\right) \left(x - 10\right)} - \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right) \left(x - 10\right)^{2}} - \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right)^{2} \left(x - 10\right)} + \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right)^{2} e^{- x}}{4 \left(x - 15\right)^{2} \left(x - 10\right)^{2}} + \frac{\sqrt{- \frac{x - 15}{x - 10}} \left(\frac{x - 15}{x - 10} - 1\right)}{4 \left(x - 15\right)^{2}} + \frac{\sqrt{- \frac{x - 15}{x - 10}}}{2 \left(x - 15\right)^{2}} + \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(x - 2\right) e^{- x} - \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(x - 1\right) \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right) \left(x - 10\right)} + \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right) \left(x - 10\right)}$$
Tercera derivada
[src]
_____________ _____________ _____________ 2 _____________
/ -(-15 + x) / -(-15 + x) / -15 + x\ / -(-15 + x) / -15 + x\ / -(-15 + x) / -15 + x\
/ ----------- 3* / ----------- *|-1 + -------| / ----------- *|-1 + -------| ______________________ -x / ----------- *|-1 + -------| ______________________ 2 -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ -x ______________________ 2 -x ______________________ 2 -x ______________________ 2 -x ______________________ 2 -x ______________________ 3 -x ______________________ -x
\/ -10 + x ______________________ -x \/ -10 + x \ -10 + x/ \/ -10 + x \ -10 + x/ 2*\/ -(-15 + x)*(-10 + x) *e \/ -10 + x \ -10 + x/ \/ -(-15 + x)*(-10 + x) *(-25 + 2*x) *e \/ -(-15 + x)*(-10 + x) *(-1 + x)*e \/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e \/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e \/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e 2*x*\/ -(-15 + x)*(-10 + x) *e 2*x*\/ -(-15 + x)*(-10 + x) *e 2*x*\/ -(-15 + x)*(-10 + x) *e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e \/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*(-2 + x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e \/ -(-15 + x)*(-10 + x) *(-1 + x)*(-25 + 2*x)*e \/ -(-15 + x)*(-10 + x) *(-1 + x)*(-25 + 2*x)*e 3*x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x) *e 3*x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x) *e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x) *e \/ -(-15 + x)*(-10 + x) *(-25 + 2*x) *(-1 + x)*e x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x) *e 5*x*\/ -(-15 + x)*(-10 + x) *(-25 + 2*x)*e
- ----------------- - \/ -(-15 + x)*(-10 + x) *(-3 + x)*e - ---------------------------------- - --------------------------------- + ------------------------------ - -------------------------------- + ----------------------------------------- - ------------------------------------- - ---------------------------------------- - ---------------------------------------- - ---------------------------------------- - -------------------------------- - -------------------------------- - -------------------------------- + ------------------------------------------ + ------------------------------------------ + ------------------------------------------ + ------------------------------------------ + ------------------------------------------------- + ------------------------------------------ + ------------------------------------------------- + ------------------------------------------------- - --------------------------------------------- - --------------------------------------------- - ------------------------------------------- - -------------------------------------------------- + ------------------------------------------- + --------------------------------------------
3 3 3 (-15 + x)*(-10 + x) 2 2 2 (-15 + x)*(-10 + x) (-15 + x)*(-10 + x) 2 2 (-15 + x)*(-10 + x) 2 2 3 2 3 2 (-15 + x)*(-10 + x) 2*(-15 + x)*(-10 + x) 2 2 3 2 2 3 2 2 2 2 3 3 2 2
(-15 + x) 4*(-15 + x) 8*(-15 + x) 4*(-15 + x) *(-10 + x) 2*(-15 + x) *(-10 + x) (-15 + x)*(-10 + x) (-15 + x) *(-10 + x) (-15 + x)*(-10 + x) (-15 + x) *(-10 + x) (-15 + x)*(-10 + x) (-15 + x)*(-10 + x) (-15 + x) *(-10 + x) (-15 + x) *(-10 + x) 2*(-15 + x)*(-10 + x) 2*(-15 + x) *(-10 + x) 4*(-15 + x) *(-10 + x) 4*(-15 + x) *(-10 + x) 2*(-15 + x) *(-10 + x) 4*(-15 + x) *(-10 + x) 8*(-15 + x) *(-10 + x) 2*(-15 + x) *(-10 + x)
$$\frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right) \left(x - 10\right)} - \frac{2 x \sqrt{- \left(x - 15\right) \left(x - 10\right)} e^{- x}}{\left(x - 15\right) \left(x - 10\right)} + \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{\left(x - 15\right) \left(x - 10\right)^{2}} - \frac{2 x \sqrt{- \left(x - 15\right) \left(x - 10\right)} e^{- x}}{\left(x - 15\right) \left(x - 10\right)^{2}} + \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{\left(x - 15\right) \left(x - 10\right)^{3}} + \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{\left(x - 15\right)^{2} \left(x - 10\right)} - \frac{2 x \sqrt{- \left(x - 15\right) \left(x - 10\right)} e^{- x}}{\left(x - 15\right)^{2} \left(x - 10\right)} - \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right)^{2} e^{- x}}{2 \left(x - 15\right)^{2} \left(x - 10\right)^{2}} + \frac{5 x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right)^{2} \left(x - 10\right)^{2}} - \frac{3 x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right)^{2} e^{- x}}{4 \left(x - 15\right)^{2} \left(x - 10\right)^{3}} + \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{\left(x - 15\right)^{3} \left(x - 10\right)} - \frac{3 x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right)^{2} e^{- x}}{4 \left(x - 15\right)^{3} \left(x - 10\right)^{2}} + \frac{x \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right)^{3} e^{- x}}{8 \left(x - 15\right)^{3} \left(x - 10\right)^{3}} - \frac{\sqrt{- \frac{x - 15}{x - 10}} \left(\frac{x - 15}{x - 10} - 1\right)}{4 \left(x - 15\right)^{2} \left(x - 10\right)} - \frac{\sqrt{- \frac{x - 15}{x - 10}} \left(\frac{x - 15}{x - 10} - 1\right)^{2}}{8 \left(x - 15\right)^{3}} - \frac{3 \sqrt{- \frac{x - 15}{x - 10}} \left(\frac{x - 15}{x - 10} - 1\right)}{4 \left(x - 15\right)^{3}} - \frac{\sqrt{- \frac{x - 15}{x - 10}}}{\left(x - 15\right)^{3}} - \sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(x - 3\right) e^{- x} + \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(x - 2\right) \left(2 x - 25\right) e^{- x}}{\left(x - 15\right) \left(x - 10\right)} - \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(x - 1\right) e^{- x}}{\left(x - 15\right) \left(x - 10\right)} - \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{\left(x - 15\right) \left(x - 10\right)} + \frac{2 \sqrt{- \left(x - 15\right) \left(x - 10\right)} e^{- x}}{\left(x - 15\right) \left(x - 10\right)} + \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(x - 1\right) \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right) \left(x - 10\right)^{2}} - \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{\left(x - 15\right) \left(x - 10\right)^{2}} + \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(x - 1\right) \left(2 x - 25\right) e^{- x}}{2 \left(x - 15\right)^{2} \left(x - 10\right)} - \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right) e^{- x}}{\left(x - 15\right)^{2} \left(x - 10\right)} - \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(x - 1\right) \left(2 x - 25\right)^{2} e^{- x}}{4 \left(x - 15\right)^{2} \left(x - 10\right)^{2}} + \frac{\sqrt{- \left(x - 15\right) \left(x - 10\right)} \left(2 x - 25\right)^{2} e^{- x}}{2 \left(x - 15\right)^{2} \left(x - 10\right)^{2}}$$