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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 y=cosx/x
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Derivative of x-e^(-x)
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Derivative of x*10^x
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Derivative of sin(x)*sin(x)*sin(x)
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Identical expressions
- arccos(x)/x
- arc co sinus of e of (x) divide by x
- arccosx/x
- arccos(x) divide by x
-
Similar expressions
- (e^arccos(x))/x+5
- (7^arccos(x))/(x+x*((x+625)^(1/2)))
- arccosx/x+0,5ln((1-sqrt(1-x^2))/(1+sqrt(1-x^2)))
- arccos(x)/(x^3-1)
- (ln(arccos(x)))/(x^2+1)
- arccosx/x
Derivative of arccos(x)/x
The solution
You have entered
[src]
acos(x) ------- x
$$\frac{\operatorname{acos}{\left(x \right)}}{x}$$
acos(x)/x
The first derivative
[src]
1 acos(x)
- ------------- - -------
________ 2
/ 2 x
x*\/ 1 - x
$$- \frac{1}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{x^{2}}$$
The second derivative
[src]
1 2*acos(x) 2
- ----------- + --------- + --------------
3/2 3 ________
/ 2\ x 2 / 2
\1 - x / x *\/ 1 - x
$$- \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{acos}{\left(x \right)}}{x^{3}}$$
The third derivative
[src]
2
3*x
-1 + -------
2
3 -1 + x 6*acos(x) 6
----------- + ------------ - --------- - --------------
3/2 3/2 3 ________
/ 2\ / 2\ x 2 / 2
\1 - x / \1 - x / x *\/ 1 - x
-------------------------------------------------------
x
$$\frac{\frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6}{x^{2} \sqrt{1 - x^{2}}} - \frac{6 \operatorname{acos}{\left(x \right)}}{x^{3}}}{x}$$