Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of x^2/cosx
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Derivative of x^2/2x+1
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Derivative of sin(x)+cot(x)
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Derivative of sin(x-(3/5))-(8/5)
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Identical expressions
- arcctg(sin(x^ two))
- arcctg( sinus of (x squared ))
- arcctg( sinus of (x to the power of two))
- arcctg(sin(x2))
- arcctgsinx2
- arcctg(sin(x²))
- arcctg(sin(x to the power of 2))
- arcctgsinx^2
Derivative of arcctg(sin(x^2))
The solution
You have entered
[src]
/ / 2\\ acot\sin\x //
$$\operatorname{acot}{\left(\sin{\left(x^{2} \right)} \right)}$$
acot(sin(x^2))
The first derivative
[src]
/ 2\
-2*x*cos\x /
------------
2/ 2\
1 + sin \x /
$$- \frac{2 x \cos{\left(x^{2} \right)}}{\sin^{2}{\left(x^{2} \right)} + 1}$$
The second derivative
[src]
/ 2 2/ 2\ / 2\\
| / 2\ 2 / 2\ 4*x *cos \x /*sin\x /|
2*|- cos\x / + 2*x *sin\x / + ---------------------|
| 2/ 2\ |
\ 1 + sin \x / /
----------------------------------------------------
2/ 2\
1 + sin \x /
$$\frac{2 \left(2 x^{2} \sin{\left(x^{2} \right)} + \frac{4 x^{2} \sin{\left(x^{2} \right)} \cos^{2}{\left(x^{2} \right)}}{\sin^{2}{\left(x^{2} \right)} + 1} - \cos{\left(x^{2} \right)}\right)}{\sin^{2}{\left(x^{2} \right)} + 1}$$
The third derivative
[src]
/ 2 3/ 2\ 2/ 2\ / 2\ 2 3/ 2\ 2/ 2\ 2 2/ 2\ / 2\\
| / 2\ 2 / 2\ 4*x *cos \x / 6*cos \x /*sin\x / 16*x *cos \x /*sin \x / 12*x *sin \x /*cos\x /|
4*x*|3*sin\x / + 2*x *cos\x / + ------------- + ------------------ - ----------------------- - ----------------------|
| 2/ 2\ 2/ 2\ 2 2/ 2\ |
| 1 + sin \x / 1 + sin \x / / 2/ 2\\ 1 + sin \x / |
\ \1 + sin \x // /
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2/ 2\
1 + sin \x /
$$\frac{4 x \left(2 x^{2} \cos{\left(x^{2} \right)} - \frac{12 x^{2} \sin^{2}{\left(x^{2} \right)} \cos{\left(x^{2} \right)}}{\sin^{2}{\left(x^{2} \right)} + 1} + \frac{4 x^{2} \cos^{3}{\left(x^{2} \right)}}{\sin^{2}{\left(x^{2} \right)} + 1} - \frac{16 x^{2} \sin^{2}{\left(x^{2} \right)} \cos^{3}{\left(x^{2} \right)}}{\left(\sin^{2}{\left(x^{2} \right)} + 1\right)^{2}} + 3 \sin{\left(x^{2} \right)} + \frac{6 \sin{\left(x^{2} \right)} \cos^{2}{\left(x^{2} \right)}}{\sin^{2}{\left(x^{2} \right)} + 1}\right)}{\sin^{2}{\left(x^{2} \right)} + 1}$$