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- Derivative of:
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Derivative of (x+3)^4
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Derivative of (x-2)^3
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Derivative of (x-2)^2*(x-4)+5
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Derivative of sqrt(x^2-1)
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Identical expressions
- log(five)^(3x+ one)^ ten
- logarithm of (5) to the power of (3x plus 1) to the power of 10
- logarithm of (five) to the power of (3x plus one) to the power of ten
- log(5)(3x+1)10
- log53x+110
- log5^3x+1^10
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Similar expressions
- log(5)^(3x-1)^10
Derivative of log(5)^(3x+1)^10
The solution
You have entered
[src]
/ 10\
\(3*x + 1) /
(log(5))
$$\log{\left(5 \right)}^{\left(3 x + 1\right)^{10}}$$
log(5)^((3*x + 1)^10)
The first derivative
[src]
/ 10\
9 \(3*x + 1) /
30*(3*x + 1) *(log(5)) *log(log(5))
$$30 \left(3 x + 1\right)^{9} \log{\left(5 \right)}^{\left(3 x + 1\right)^{10}} \log{\left(\log{\left(5 \right)} \right)}$$
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))
$$90 \left(3 x + 1\right)^{8} \left(10 \left(3 x + 1\right)^{10} \log{\left(\log{\left(5 \right)} \right)} + 9\right) \log{\left(5 \right)}^{\left(3 x + 1\right)^{10}} \log{\left(\log{\left(5 \right)} \right)}$$
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))
$$540 \left(3 x + 1\right)^{7} \left(50 \left(3 x + 1\right)^{20} \log{\left(\log{\left(5 \right)} \right)}^{2} + 135 \left(3 x + 1\right)^{10} \log{\left(\log{\left(5 \right)} \right)} + 36\right) \log{\left(5 \right)}^{\left(3 x + 1\right)^{10}} \log{\left(\log{\left(5 \right)} \right)}$$