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 ln(1+x)
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Derivative of sqrt(y)
- Derivative of i*n*sin(x)
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Derivative of e^sin(x)
- Equation:
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(arccosx)/(arcsinx^2)
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Identical expressions
- (arccosx)/(arcsinx^ two)
- (arc co sinus of e of x) divide by (arc sinus of x squared )
- (arc co sinus of e of x) divide by (arc sinus of x to the power of two)
- (arccosx)/(arcsinx2)
- arccosx/arcsinx2
- (arccosx)/(arcsinx²)
- (arccosx)/(arcsinx to the power of 2)
- arccosx/arcsinx^2
- (arccosx) divide by (arcsinx^2)
Derivative of (arccosx)/(arcsinx^2)
The solution
You have entered
[src]
acos(x)
--------
2
asin (x)
$$\frac{\operatorname{acos}{\left(x \right)}}{\operatorname{asin}^{2}{\left(x \right)}}$$
acos(x)/asin(x)^2
The first derivative
[src]
1 2*acos(x)
- -------------------- - --------------------
________ ________
/ 2 2 / 2 3
\/ 1 - x *asin (x) \/ 1 - x *asin (x)
$$- \frac{2 \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{3}{\left(x \right)}} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}$$
The second derivative
[src]
/ / x 3 \ \
| 2*|----------- + -----------------|*acos(x)|
| | 3/2 / 2\ | |
| |/ 2\ \-1 + x /*asin(x)| |
| x 4 \\1 - x / / |
-|----------- + ----------------- + -------------------------------------------|
| 3/2 / 2\ asin(x) |
|/ 2\ \-1 + x /*asin(x) |
\\1 - x / /
---------------------------------------------------------------------------------
2
asin (x)
$$- \frac{\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{4}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}}{\operatorname{asin}^{2}{\left(x \right)}}$$
The third derivative
[src]
/ 2 \
2 | 1 3*x 12 9*x | / x 3 \
3*x 2*|----------- + ----------- + -------------------- - ------------------|*acos(x) 6*|----------- + -----------------|
-1 + ------- | 3/2 5/2 3/2 2 | | 3/2 / 2\ |
2 |/ 2\ / 2\ / 2\ 2 / 2\ | |/ 2\ \-1 + x /*asin(x)|
-1 + x \\1 - x / \1 - x / \1 - x / *asin (x) \-1 + x / *asin(x)/ 6*x \\1 - x / /
------------ - --------------------------------------------------------------------------------- + ------------------ + -----------------------------------
3/2 asin(x) 2 ________
/ 2\ / 2\ / 2
\1 - x / \-1 + x / *asin(x) \/ 1 - x *asin(x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------
2
asin (x)
$$\frac{\frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} - \frac{2 \left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{9 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{12}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{6 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right)}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{\operatorname{asin}^{2}{\left(x \right)}}$$
The graph