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The derivative of the function/ (x+3)^sin5x

Derivative of (x+3)^sin5x

Function f() - derivative -N order at the point
v

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from to

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The solution

You have entered [src] 
       sin(5*x)
(x + 3)
$$\left(x + 3\right)^{\sin{\left(5 x \right)}}$$ 
(x + 3)^sin(5*x)
Detail solution

  1. Don't know the steps in finding this derivative.

    But the derivative is

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       sin(5*x) /sin(5*x)                        \
(x + 3)        *|-------- + 5*cos(5*x)*log(x + 3)|
                \ x + 3                          /
$$\left(x + 3\right)^{\sin{\left(5 x \right)}} \left(5 \log{\left(x + 3 \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x + 3}\right)$$
Simplify
The second derivative [src] 
                /                                  2                                                  \
       sin(5*x) |/sin(5*x)                        \    sin(5*x)                            10*cos(5*x)|
(3 + x)        *||-------- + 5*cos(5*x)*log(3 + x)|  - -------- - 25*log(3 + x)*sin(5*x) + -----------|
                |\ 3 + x                          /           2                               3 + x   |
                \                                      (3 + x)                                        /
$$\left(x + 3\right)^{\sin{\left(5 x \right)}} \left(\left(5 \log{\left(x + 3 \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x + 3}\right)^{2} - 25 \log{\left(x + 3 \right)} \sin{\left(5 x \right)} + \frac{10 \cos{\left(5 x \right)}}{x + 3} - \frac{\sin{\left(5 x \right)}}{\left(x + 3\right)^{2}}\right)$$
Simplify
The third derivative [src] 
                /                                  3                                                                                                                                                            \
       sin(5*x) |/sin(5*x)                        \                              75*sin(5*x)   15*cos(5*x)     /sin(5*x)                        \ /sin(5*x)   10*cos(5*x)                         \   2*sin(5*x)|
(3 + x)        *||-------- + 5*cos(5*x)*log(3 + x)|  - 125*cos(5*x)*log(3 + x) - ----------- - ----------- - 3*|-------- + 5*cos(5*x)*log(3 + x)|*|-------- - ----------- + 25*log(3 + x)*sin(5*x)| + ----------|
                |\ 3 + x                          /                                 3 + x               2      \ 3 + x                          / |       2      3 + x                            |           3 |
                \                                                                                (3 + x)                                          \(3 + x)                                        /    (3 + x)  /
$$\left(x + 3\right)^{\sin{\left(5 x \right)}} \left(\left(5 \log{\left(x + 3 \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x + 3}\right)^{3} - 3 \left(5 \log{\left(x + 3 \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x + 3}\right) \left(25 \log{\left(x + 3 \right)} \sin{\left(5 x \right)} - \frac{10 \cos{\left(5 x \right)}}{x + 3} + \frac{\sin{\left(5 x \right)}}{\left(x + 3\right)^{2}}\right) - 125 \log{\left(x + 3 \right)} \cos{\left(5 x \right)} - \frac{75 \sin{\left(5 x \right)}}{x + 3} - \frac{15 \cos{\left(5 x \right)}}{\left(x + 3\right)^{2}} + \frac{2 \sin{\left(5 x \right)}}{\left(x + 3\right)^{3}}\right)$$
Simplify
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