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