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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of x^e
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Derivative of (x^3-1)(x^2+x+1)
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Derivative of ln1
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Derivative of (5*x-4)*(2*x^4-7*x+1)
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Identical expressions
- ctg(3x)^(two *x)
- ctg(3x) to the power of (2 multiply by x)
- ctg(3x) to the power of (two multiply by x)
- ctg(3x)(2*x)
- ctg3x2*x
- ctg(3x)^(2x)
- ctg(3x)(2x)
- ctg3x2x
- ctg3x^2x
Derivative of ctg(3x)^(2*x)
The solution
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[src]
2*x cot (3*x)
$$\cot^{2 x}{\left(3 x \right)}$$
d / 2*x \ --\cot (3*x)/ dx
$$\frac{d}{d x} \cot^{2 x}{\left(3 x \right)}$$
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
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/ / 2 \\
2*x | 2*x*\-3 - 3*cot (3*x)/|
cot (3*x)*|2*log(cot(3*x)) + ----------------------|
\ cot(3*x) /
$$\left(\frac{2 x \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right)}{\cot{\left(3 x \right)}} + 2 \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{2 x}{\left(3 x \right)}$$
The second derivative
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/ 2 \
| / / 2 \\ / / 2 \\|
2*x | | 3*x*\1 + cot (3*x)/| / 2 \ | 2 3*x*\1 + cot (3*x)/||
2*cot (3*x)*|2*|-log(cot(3*x)) + -------------------| - 3*\1 + cot (3*x)/*|-6*x + -------- + -------------------||
| \ cot(3*x) / | cot(3*x) 2 ||
\ \ cot (3*x) //
$$2 \cdot \left(2 \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(\cot{\left(3 x \right)} \right)}\right)^{2} - 3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot^{2}{\left(3 x \right)}} - 6 x + \frac{2}{\cot{\left(3 x \right)}}\right)\right) \cot^{2 x}{\left(3 x \right)}$$
The third derivative
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/ 3 2 3 2\
| / / 2 \\ / 2 \ / 2 \ / / 2 \\ / / 2 \\ / 2 \ |
2*x | | 3*x*\1 + cot (3*x)/| 2 27*\1 + cot (3*x)/ / 2 \ 54*x*\1 + cot (3*x)/ / 2 \ | 3*x*\1 + cot (3*x)/| | 2 3*x*\1 + cot (3*x)/| 108*x*\1 + cot (3*x)/ |
2*cot (3*x)*|54 - 4*|-log(cot(3*x)) + -------------------| + 54*cot (3*x) - ------------------- - 108*x*\1 + cot (3*x)/*cot(3*x) - --------------------- + 18*\1 + cot (3*x)/*|-log(cot(3*x)) + -------------------|*|-6*x + -------- + -------------------| + ----------------------|
| \ cot(3*x) / 2 3 \ cot(3*x) / | cot(3*x) 2 | cot(3*x) |
\ cot (3*x) cot (3*x) \ cot (3*x) / /
$$2 \left(- \frac{54 x \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3}}{\cot^{3}{\left(3 x \right)}} + \frac{108 x \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot{\left(3 x \right)}} - 108 x \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} - 4 \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(\cot{\left(3 x \right)} \right)}\right)^{3} + 18 \cdot \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(\cot{\left(3 x \right)} \right)}\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot^{2}{\left(3 x \right)}} - 6 x + \frac{2}{\cot{\left(3 x \right)}}\right) - \frac{27 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} + 54 \cot^{2}{\left(3 x \right)} + 54\right) \cot^{2 x}{\left(3 x \right)}$$
The graph