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 sin(x)/(1+cos(x))
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Derivative of f(x)=x
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Derivative of ln(lnx)
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Derivative of f
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Identical expressions
- asin(x)/acos(x)
- arc sinus of e of (x) divide by arc co sinus of e of ine of (x)
- asinx/acosx
- asin(x) divide by acos(x)
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Similar expressions
- 6*sqrt((asin(x))/(acos(x)))
- arcsin(x)/arccos(x)
- arcsinx/arccosx
Derivative of asin(x)/acos(x)
The solution
You have entered
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asin(x) ------- acos(x)
$$\frac{\operatorname{asin}{\left(x \right)}}{\operatorname{acos}{\left(x \right)}}$$
asin(x)/acos(x)
The first derivative
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1 asin(x) ------------------- + -------------------- ________ ________ / 2 / 2 2 \/ 1 - x *acos(x) \/ 1 - x *acos (x)
$$\frac{1}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}$$
The second derivative
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/ x 2 \
|----------- - -----------------|*asin(x)
| 3/2 / 2\ |
|/ 2\ \-1 + x /*acos(x)|
x 2 \\1 - x / /
----------- - ----------------- + -----------------------------------------
3/2 / 2\ acos(x)
/ 2\ \-1 + x /*acos(x)
\1 - x /
---------------------------------------------------------------------------
acos(x)
$$\frac{\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{acos}{\left(x \right)}}\right) \operatorname{asin}{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{acos}{\left(x \right)}}}{\operatorname{acos}{\left(x \right)}}$$
The third derivative
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/ 2 \
2 | 1 3*x 6 6*x | / x 2 \
3*x |----------- + ----------- + -------------------- + ------------------|*asin(x) 3*|----------- - -----------------|
-1 + ------- | 3/2 5/2 3/2 2 | | 3/2 / 2\ |
2 |/ 2\ / 2\ / 2\ 2 / 2\ | |/ 2\ \-1 + x /*acos(x)|
-1 + x \\1 - x / \1 - x / \1 - x / *acos (x) \-1 + x / *acos(x)/ 3*x \\1 - x / /
- ------------ + ------------------------------------------------------------------------------- + ------------------ + -----------------------------------
3/2 acos(x) 2 ________
/ 2\ / 2\ / 2
\1 - x / \-1 + x / *acos(x) \/ 1 - x *acos(x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------
acos(x)
$$\frac{\frac{3 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}{\left(x \right)}} + \frac{\left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}{\left(x \right)}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(x \right)}}\right) \operatorname{asin}{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} + \frac{3 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{acos}{\left(x \right)}}\right)}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{\operatorname{acos}{\left(x \right)}}$$
The graph