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The derivative of the function/ log(5)^(3x+1)^10

Derivative of log(5)^(3x+1)^10

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

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The solution

You have entered [src] 
        /         10\
        \(3*x + 1)  /
(log(5))
log⁡(5)(3x+1)10\log{\left(5 \right)}^{\left(3 x + 1\right)^{10}} 
log(5)^((3*x + 1)^10)
The first derivative [src] 
                      /         10\            
            9         \(3*x + 1)  /            
30*(3*x + 1) *(log(5))             *log(log(5))
30(3x+1)9log⁡(5)(3x+1)10log⁡(log⁡(5))30 \left(3 x + 1\right)^{9} \log{\left(5 \right)}^{\left(3 x + 1\right)^{10}} \log{\left(\log{\left(5 \right)} \right)}
Simplify
The second derivative [src] 
                      /         10\                                             
            8         \(1 + 3*x)  / /                10            \            
90*(1 + 3*x) *(log(5))             *\9 + 10*(1 + 3*x)  *log(log(5))/*log(log(5))
90(3x+1)8(10(3x+1)10log⁡(log⁡(5))+9)log⁡(5)(3x+1)10log⁡(log⁡(5))90 \left(3 x + 1\right)^{8} \left(10 \left(3 x + 1\right)^{10} \log{\left(\log{\left(5 \right)} \right)} + 9\right) \log{\left(5 \right)}^{\left(3 x + 1\right)^{10}} \log{\left(\log{\left(5 \right)} \right)}
Simplify
The third derivative [src] 
                       /         10\                                                                             
             7         \(1 + 3*x)  / /                 20    2                        10            \            
540*(1 + 3*x) *(log(5))             *\36 + 50*(1 + 3*x)  *log (log(5)) + 135*(1 + 3*x)  *log(log(5))/*log(log(5))
540(3x+1)7(50(3x+1)20log⁡(log⁡(5))2+135(3x+1)10log⁡(log⁡(5))+36)log⁡(5)(3x+1)10log⁡(log⁡(5))540 \left(3 x + 1\right)^{7} \left(50 \left(3 x + 1\right)^{20} \log{\left(\log{\left(5 \right)} \right)}^{2} + 135 \left(3 x + 1\right)^{10} \log{\left(\log{\left(5 \right)} \right)} + 36\right) \log{\left(5 \right)}^{\left(3 x + 1\right)^{10}} \log{\left(\log{\left(5 \right)} \right)}
Simplify
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