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The derivative of the function/ (6*x-8)^(cos(x))

Derivative of (6*x-8)^(cos(x))

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

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The solution

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         cos(x)
(6*x - 8)
$$\left(6 x - 8\right)^{\cos{\left(x \right)}}$$ 
(6*x - 8)^cos(x)
Detail solution

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The graph
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The first derivative [src] 
         cos(x) /                       6*cos(x)\
(6*x - 8)      *|-log(6*x - 8)*sin(x) + --------|
                \                       6*x - 8 /
$$\left(6 x - 8\right)^{\cos{\left(x \right)}} \left(- \log{\left(6 x - 8 \right)} \sin{\left(x \right)} + \frac{6 \cos{\left(x \right)}}{6 x - 8}\right)$$
Simplify
The second derivative [src] 
                     /                                     2                                                    \
              cos(x) |/                           3*cos(x)\                                 9*cos(x)    6*sin(x)|
(2*(-4 + 3*x))      *||log(2*(-4 + 3*x))*sin(x) - --------|  - cos(x)*log(2*(-4 + 3*x)) - ----------- - --------|
                     |\                           -4 + 3*x/                                         2   -4 + 3*x|
                     \                                                                    (-4 + 3*x)            /
$$\left(2 \left(3 x - 4\right)\right)^{\cos{\left(x \right)}} \left(\left(\log{\left(2 \left(3 x - 4\right) \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{3 x - 4}\right)^{2} - \log{\left(2 \left(3 x - 4\right) \right)} \cos{\left(x \right)} - \frac{6 \sin{\left(x \right)}}{3 x - 4} - \frac{9 \cos{\left(x \right)}}{\left(3 x - 4\right)^{2}}\right)$$
Simplify
The third derivative [src] 
                     /                                       3                                                                                                                                                                \
              cos(x) |  /                           3*cos(x)\                               9*cos(x)     /                           3*cos(x)\ /                           6*sin(x)     9*cos(x) \    27*sin(x)     54*cos(x) |
(2*(-4 + 3*x))      *|- |log(2*(-4 + 3*x))*sin(x) - --------|  + log(2*(-4 + 3*x))*sin(x) - -------- + 3*|log(2*(-4 + 3*x))*sin(x) - --------|*|cos(x)*log(2*(-4 + 3*x)) + -------- + -----------| + ----------- + -----------|
                     |  \                           -4 + 3*x/                               -4 + 3*x     \                           -4 + 3*x/ |                           -4 + 3*x             2|             2             3|
                     \                                                                                                                         \                                      (-4 + 3*x) /   (-4 + 3*x)    (-4 + 3*x) /
$$\left(2 \left(3 x - 4\right)\right)^{\cos{\left(x \right)}} \left(- \left(\log{\left(2 \left(3 x - 4\right) \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{3 x - 4}\right)^{3} + 3 \left(\log{\left(2 \left(3 x - 4\right) \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{3 x - 4}\right) \left(\log{\left(2 \left(3 x - 4\right) \right)} \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{3 x - 4} + \frac{9 \cos{\left(x \right)}}{\left(3 x - 4\right)^{2}}\right) + \log{\left(2 \left(3 x - 4\right) \right)} \sin{\left(x \right)} - \frac{9 \cos{\left(x \right)}}{3 x - 4} + \frac{27 \sin{\left(x \right)}}{\left(3 x - 4\right)^{2}} + \frac{54 \cos{\left(x \right)}}{\left(3 x - 4\right)^{3}}\right)$$
Simplify
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