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 sin(x)^2
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Derivative of sin(9x+2)
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Derivative of 4*x-4
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Derivative of 3*(t-sin(t))
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Identical expressions
- arcsin(sin(x)^ two)
- arc sinus of ( sinus of (x) squared )
- arc sinus of ( sinus of (x) to the power of two)
- arcsin(sin(x)2)
- arcsinsinx2
- arcsin(sin(x)²)
- arcsin(sin(x) to the power of 2)
- arcsinsinx^2
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Similar expressions
- arcsin(sinx^2)
Derivative of arcsin(sin(x)^2)
The solution
You have entered
[src]
/ 2 \ asin\sin (x)/
$$\operatorname{asin}{\left(\sin^{2}{\left(x \right)} \right)}$$
asin(sin(x)^2)
The first derivative
[src]
2*cos(x)*sin(x) ---------------- _____________ / 4 \/ 1 - sin (x)
$$\frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{1 - \sin^{4}{\left(x \right)}}}$$
The second derivative
[src]
/ 2 4 \
| 2 2 2*cos (x)*sin (x)|
2*|cos (x) - sin (x) + -----------------|
| 4 |
\ 1 - sin (x) /
-----------------------------------------
_____________
/ 4
\/ 1 - sin (x)
$$\frac{2 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} + \frac{2 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{1 - \sin^{4}{\left(x \right)}}\right)}{\sqrt{1 - \sin^{4}{\left(x \right)}}}$$
The third derivative
[src]
/ 4 2 2 2 6 \
| 3*sin (x) 5*cos (x)*sin (x) 6*cos (x)*sin (x)|
4*|-2 - ----------- + ----------------- + -----------------|*cos(x)*sin(x)
| 4 4 2 |
| 1 - sin (x) 1 - sin (x) / 4 \ |
\ \1 - sin (x)/ /
--------------------------------------------------------------------------
_____________
/ 4
\/ 1 - sin (x)
$$\frac{4 \left(-2 - \frac{3 \sin^{4}{\left(x \right)}}{1 - \sin^{4}{\left(x \right)}} + \frac{5 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{1 - \sin^{4}{\left(x \right)}} + \frac{6 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(1 - \sin^{4}{\left(x \right)}\right)^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{1 - \sin^{4}{\left(x \right)}}}$$