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y=(7+e^(2x))^sqrt(x-3)

Derivada de y=(7+e^(2x))^sqrt(x-3)

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Solución

Ha introducido [src]
            _______
          \/ x - 3 
/     2*x\         
\7 + E   /         
$$\left(e^{2 x} + 7\right)^{\sqrt{x - 3}}$$
(7 + E^(2*x))^(sqrt(x - 3))
Solución detallada
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    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
            _______                                   
          \/ x - 3  /   /     2*x\       _______  2*x\
/     2*x\          |log\7 + E   /   2*\/ x - 3 *e   |
\7 + E   /         *|------------- + ----------------|
                    |     _______             2*x    |
                    \ 2*\/ x - 3         7 + E       /
$$\left(e^{2 x} + 7\right)^{\sqrt{x - 3}} \left(\frac{\log{\left(e^{2 x} + 7 \right)}}{2 \sqrt{x - 3}} + \frac{2 \sqrt{x - 3} e^{2 x}}{e^{2 x} + 7}\right)$$
Segunda derivada [src]
                     /                                   2                                                                                \
                     |/   /     2*x\       ________  2*x\                                                                                 |
                     ||log\7 + e   /   4*\/ -3 + x *e   |                                                                                 |
            ________ ||------------- + -----------------|                                                                                 |
          \/ -3 + x  ||    ________              2*x    |       /     2*x\       ________  4*x              2*x              ________  2*x|
/     2*x\           |\  \/ -3 + x          7 + e       /    log\7 + e   /   4*\/ -3 + x *e              2*e             4*\/ -3 + x *e   |
\7 + e   /          *|------------------------------------ - ------------- - ----------------- + --------------------- + -----------------|
                     |                 4                               3/2                2        ________ /     2*x\             2*x    |
                     |                                       4*(-3 + x)         /     2*x\       \/ -3 + x *\7 + e   /        7 + e       |
                     \                                                          \7 + e   /                                                /
$$\left(e^{2 x} + 7\right)^{\sqrt{x - 3}} \left(\frac{4 \sqrt{x - 3} e^{2 x}}{e^{2 x} + 7} - \frac{4 \sqrt{x - 3} e^{4 x}}{\left(e^{2 x} + 7\right)^{2}} + \frac{\left(\frac{4 \sqrt{x - 3} e^{2 x}}{e^{2 x} + 7} + \frac{\log{\left(e^{2 x} + 7 \right)}}{\sqrt{x - 3}}\right)^{2}}{4} + \frac{2 e^{2 x}}{\sqrt{x - 3} \left(e^{2 x} + 7\right)} - \frac{\log{\left(e^{2 x} + 7 \right)}}{4 \left(x - 3\right)^{\frac{3}{2}}}\right)$$
Tercera derivada [src]
                     /                                   3     /   /     2*x\       ________  2*x\ /   /     2*x\        ________  2*x              2*x               ________  4*x\                                                                                                                                                            \
                     |/   /     2*x\       ________  2*x\      |log\7 + e   /   4*\/ -3 + x *e   | |log\7 + e   /   16*\/ -3 + x *e              8*e             16*\/ -3 + x *e   |                                                                                                                                                            |
                     ||log\7 + e   /   4*\/ -3 + x *e   |    3*|------------- + -----------------|*|------------- - ------------------ - --------------------- + ------------------|                                                                                                                                                            |
            ________ ||------------- + -----------------|      |    ________              2*x    | |         3/2              2*x          ________ /     2*x\                2    |                                                                                                                                                            |
          \/ -3 + x  ||    ________              2*x    |      \  \/ -3 + x          7 + e       / | (-3 + x)            7 + e           \/ -3 + x *\7 + e   /      /     2*x\     |        /     2*x\        ________  4*x              4*x                      2*x              ________  2*x        ________  6*x               2*x         |
/     2*x\           |\  \/ -3 + x          7 + e       /                                          \                                                                \7 + e   /     /   3*log\7 + e   /   24*\/ -3 + x *e              6*e                      6*e             8*\/ -3 + x *e      16*\/ -3 + x *e               3*e            |
\7 + e   /          *|------------------------------------ - ----------------------------------------------------------------------------------------------------------------------- + --------------- - ------------------ - ---------------------- + --------------------- + ----------------- + ------------------ - ------------------------|
                     |                 8                                                                                8                                                                         5/2                 2                            2     ________ /     2*x\             2*x                    3                 3/2 /     2*x\|
                     |                                                                                                                                                                  8*(-3 + x)          /     2*x\          ________ /     2*x\    \/ -3 + x *\7 + e   /        7 + e             /     2*x\        2*(-3 + x)   *\7 + e   /|
                     \                                                                                                                                                                                      \7 + e   /        \/ -3 + x *\7 + e   /                                                   \7 + e   /                                /
$$\left(e^{2 x} + 7\right)^{\sqrt{x - 3}} \left(\frac{8 \sqrt{x - 3} e^{2 x}}{e^{2 x} + 7} - \frac{24 \sqrt{x - 3} e^{4 x}}{\left(e^{2 x} + 7\right)^{2}} + \frac{16 \sqrt{x - 3} e^{6 x}}{\left(e^{2 x} + 7\right)^{3}} + \frac{\left(\frac{4 \sqrt{x - 3} e^{2 x}}{e^{2 x} + 7} + \frac{\log{\left(e^{2 x} + 7 \right)}}{\sqrt{x - 3}}\right)^{3}}{8} - \frac{3 \left(\frac{4 \sqrt{x - 3} e^{2 x}}{e^{2 x} + 7} + \frac{\log{\left(e^{2 x} + 7 \right)}}{\sqrt{x - 3}}\right) \left(- \frac{16 \sqrt{x - 3} e^{2 x}}{e^{2 x} + 7} + \frac{16 \sqrt{x - 3} e^{4 x}}{\left(e^{2 x} + 7\right)^{2}} - \frac{8 e^{2 x}}{\sqrt{x - 3} \left(e^{2 x} + 7\right)} + \frac{\log{\left(e^{2 x} + 7 \right)}}{\left(x - 3\right)^{\frac{3}{2}}}\right)}{8} + \frac{6 e^{2 x}}{\sqrt{x - 3} \left(e^{2 x} + 7\right)} - \frac{6 e^{4 x}}{\sqrt{x - 3} \left(e^{2 x} + 7\right)^{2}} - \frac{3 e^{2 x}}{2 \left(x - 3\right)^{\frac{3}{2}} \left(e^{2 x} + 7\right)} + \frac{3 \log{\left(e^{2 x} + 7 \right)}}{8 \left(x - 3\right)^{\frac{5}{2}}}\right)$$
Gráfico
Derivada de y=(7+e^(2x))^sqrt(x-3)