Mister Exam
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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+3)^4
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Derivative of x^2+3x
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Derivative of x^2-3*x+2
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Derivative of (x-2)^2*(x-4)+5
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Identical expressions
- arcsin(ctg(three ^x))
- arc sinus of (ctg(3 to the power of x))
- arc sinus of (ctg(three to the power of x))
- arcsin(ctg(3x))
- arcsinctg3x
- arcsinctg3^x
Derivative of arcsin(ctg(3^x))
The solution
You have entered
[src]
/ / x\\ asin\cot\3 //
$$\operatorname{asin}{\left(\cot{\left(3^{x} \right)} \right)}$$
asin(cot(3^x))
The first derivative
[src]
x / 2/ x\\
3 *\-1 - cot \3 //*log(3)
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______________
/ 2/ x\
\/ 1 - cot \3 /
$$\frac{3^{x} \left(- \cot^{2}{\left(3^{x} \right)} - 1\right) \log{\left(3 \right)}}{\sqrt{1 - \cot^{2}{\left(3^{x} \right)}}}$$
The second derivative
[src]
/ x / 2/ x\\ / x\\
x 2 / 2/ x\\ | x / x\ 3 *\1 + cot \3 //*cot\3 /|
3 *log (3)*\1 + cot \3 //*|-1 + 2*3 *cot\3 / + -------------------------|
| 2/ x\ |
\ 1 - cot \3 / /
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______________
/ 2/ x\
\/ 1 - cot \3 /
$$\frac{3^{x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \left(2 \cdot 3^{x} \cot{\left(3^{x} \right)} + \frac{3^{x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \cot{\left(3^{x} \right)}}{1 - \cot^{2}{\left(3^{x} \right)}} - 1\right) \log{\left(3 \right)}^{2}}{\sqrt{1 - \cot^{2}{\left(3^{x} \right)}}}$$
The third derivative
[src]
/ 2 2 \
| 2*x / 2/ x\\ 2*x 2/ x\ / 2/ x\\ 2*x / 2/ x\\ 2/ x\ x / 2/ x\\ / x\|
x 3 / 2/ x\\ | 2*x 2/ x\ 2*x / 2/ x\\ x / x\ 3 *\1 + cot \3 // 6*3 *cot \3 /*\1 + cot \3 // 3*3 *\1 + cot \3 // *cot \3 / 3*3 *\1 + cot \3 //*cot\3 /|
3 *log (3)*\1 + cot \3 //*|-1 - 4*3 *cot \3 / - 2*3 *\1 + cot \3 // + 6*3 *cot\3 / - -------------------- - ------------------------------ - ------------------------------- + ---------------------------|
| 2/ x\ 2/ x\ 2 2/ x\ |
| 1 - cot \3 / 1 - cot \3 / / 2/ x\\ 1 - cot \3 / |
\ \1 - cot \3 // /
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______________
/ 2/ x\
\/ 1 - cot \3 /
$$\frac{3^{x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \left(- 2 \cdot 3^{2 x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) - 4 \cdot 3^{2 x} \cot^{2}{\left(3^{x} \right)} - \frac{3^{2 x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right)^{2}}{1 - \cot^{2}{\left(3^{x} \right)}} - \frac{6 \cdot 3^{2 x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \cot^{2}{\left(3^{x} \right)}}{1 - \cot^{2}{\left(3^{x} \right)}} - \frac{3 \cdot 3^{2 x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right)^{2} \cot^{2}{\left(3^{x} \right)}}{\left(1 - \cot^{2}{\left(3^{x} \right)}\right)^{2}} + 6 \cdot 3^{x} \cot{\left(3^{x} \right)} + \frac{3 \cdot 3^{x} \left(\cot^{2}{\left(3^{x} \right)} + 1\right) \cot{\left(3^{x} \right)}}{1 - \cot^{2}{\left(3^{x} \right)}} - 1\right) \log{\left(3 \right)}^{3}}{\sqrt{1 - \cot^{2}{\left(3^{x} \right)}}}$$