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How to use it?
- Derivative of:
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Derivative of f(x)=4x^2
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Derivative of 7*x+5
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Derivative of (x-1)^4(x+1)^7
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Derivative of tan(x)*(x-4)
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Identical expressions
- arccosx/(x-arcsinx)
- arc co sinus of e of x divide by (x minus arc sinus of x)
- arccosx/x-arcsinx
- arccosx divide by (x-arcsinx)
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Similar expressions
- arccosx/(x+arcsinx)
Derivative of arccosx/(x-arcsinx)
The solution
You have entered
[src]
acos(x) ----------- x - asin(x)
$$\frac{\operatorname{acos}{\left(x \right)}}{x - \operatorname{asin}{\left(x \right)}}$$
acos(x)/(x - asin(x))
The first derivative
[src]
/ 1 \
|-1 + -----------|*acos(x)
| ________|
| / 2 |
1 \ \/ 1 - x /
- ------------------------- + --------------------------
________ 2
/ 2 (x - asin(x))
\/ 1 - x *(x - asin(x))
$$\frac{\left(-1 + \frac{1}{\sqrt{1 - x^{2}}}\right) \operatorname{acos}{\left(x \right)}}{\left(x - \operatorname{asin}{\left(x \right)}\right)^{2}} - \frac{1}{\sqrt{1 - x^{2}} \left(x - \operatorname{asin}{\left(x \right)}\right)}$$
The second derivative
[src]
/ 2\
| / 1 \ |
| 2*|1 - -----------| |
| | ________| |
| | / 2 | |
| x \ \/ 1 - x / | / 1 \
|----------- + --------------------|*acos(x) 2*|1 - -----------|
| 3/2 x - asin(x) | | ________|
|/ 2\ | | / 2 |
x \\1 - x / / \ \/ 1 - x /
- ----------- + -------------------------------------------- + -------------------------
3/2 x - asin(x) ________
/ 2\ / 2
\1 - x / \/ 1 - x *(x - asin(x))
----------------------------------------------------------------------------------------
x - asin(x)
$$\frac{- \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{2}}{x - \operatorname{asin}{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)}}{x - \operatorname{asin}{\left(x \right)}} + \frac{2 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)}{\sqrt{1 - x^{2}} \left(x - \operatorname{asin}{\left(x \right)}\right)}}{x - \operatorname{asin}{\left(x \right)}}$$
The third derivative
[src]
/ 3 \ / 2\
| / 1 \ / 1 \ | | / 1 \ |
| 6*|1 - -----------| 6*x*|1 - -----------| | | 2*|1 - -----------| |
| | ________| | ________| | | | ________| |
| | / 2 | 2 | / 2 | | | | / 2 | |
2 | 1 \ \/ 1 - x / 3*x \ \/ 1 - x / | | x \ \/ 1 - x / | / 1 \
3*x |----------- - -------------------- + ----------- - -------------------------|*acos(x) 3*|----------- + --------------------| 3*x*|1 - -----------|
-1 + ------- | 3/2 2 5/2 3/2 | | 3/2 x - asin(x) | | ________|
2 |/ 2\ (x - asin(x)) / 2\ / 2\ | |/ 2\ | | / 2 |
-1 + x \\1 - x / \1 - x / \1 - x / *(x - asin(x))/ \\1 - x / / \ \/ 1 - x /
------------ + -------------------------------------------------------------------------------------- - -------------------------------------- + -------------------------
3/2 x - asin(x) ________ 3/2
/ 2\ / 2 / 2\
\1 - x / \/ 1 - x *(x - asin(x)) \1 - x / *(x - asin(x))
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x - asin(x)
$$\frac{\frac{3 x \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x - \operatorname{asin}{\left(x \right)}\right)} + \frac{\left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{6 x \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x - \operatorname{asin}{\left(x \right)}\right)} - \frac{6 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{3}}{\left(x - \operatorname{asin}{\left(x \right)}\right)^{2}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \operatorname{acos}{\left(x \right)}}{x - \operatorname{asin}{\left(x \right)}} - \frac{3 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{2}}{x - \operatorname{asin}{\left(x \right)}}\right)}{\sqrt{1 - x^{2}} \left(x - \operatorname{asin}{\left(x \right)}\right)} + \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{x - \operatorname{asin}{\left(x \right)}}$$