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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of arctg(1/x)
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Derivative of e^cos(x)
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Derivative of ln(x+3)^3
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Derivative of cot(1/x)
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Identical expressions
- sin(x)**asin(x)
- sinus of (x) multiply by multiply by arc sinus of e of (x)
- sin(x)asin(x)
- sinxasinx
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Similar expressions
- sin(x)**arcsin(x)
- sinx**arcsinx
Derivative of sin(x)**asin(x)
The solution
You have entered
[src]
asin(x) sin (x)
$$\sin^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}$$
sin(x)^asin(x)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
asin(x) /log(sin(x)) asin(x)*cos(x)\
sin (x)*|----------- + --------------|
| ________ sin(x) |
| / 2 |
\\/ 1 - x /
$$\left(\frac{\cos{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \sin^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}$$
The second derivative
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/ 2 2 \
asin(x) |/log(sin(x)) asin(x)*cos(x)\ x*log(sin(x)) cos (x)*asin(x) 2*cos(x) |
sin (x)*||----------- + --------------| - asin(x) + ------------- - --------------- + ------------------|
|| ________ sin(x) | 3/2 2 ________ |
|| / 2 | / 2\ sin (x) / 2 |
\\\/ 1 - x / \1 - x / \/ 1 - x *sin(x)/
$$\left(\frac{x \log{\left(\sin{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\cos{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}}\right)^{2} - \operatorname{asin}{\left(x \right)} - \frac{\cos^{2}{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{\sqrt{1 - x^{2}} \sin{\left(x \right)}}\right) \sin^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}$$
The third derivative
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/ 3 / 2 \ 2 3 2 \
asin(x) |/log(sin(x)) asin(x)*cos(x)\ 3 log(sin(x)) /log(sin(x)) asin(x)*cos(x)\ | x*log(sin(x)) cos (x)*asin(x) 2*cos(x) | 3*cos (x) 2*cos (x)*asin(x) 2*asin(x)*cos(x) 3*x *log(sin(x)) 3*x*cos(x) |
sin (x)*||----------- + --------------| - ----------- + ----------- + 3*|----------- + --------------|*|-asin(x) + ------------- - --------------- + ------------------| - ------------------- + ----------------- + ---------------- + ---------------- + ------------------|
|| ________ sin(x) | ________ 3/2 | ________ sin(x) | | 3/2 2 ________ | ________ 3 sin(x) 5/2 3/2 |
|| / 2 | / 2 / 2\ | / 2 | | / 2\ sin (x) / 2 | / 2 2 sin (x) / 2\ / 2\ |
\\\/ 1 - x / \/ 1 - x \1 - x / \\/ 1 - x / \ \1 - x / \/ 1 - x *sin(x)/ \/ 1 - x *sin (x) \1 - x / \1 - x / *sin(x)/
$$\left(\frac{3 x^{2} \log{\left(\sin{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x \cos{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \sin{\left(x \right)}} + \left(\frac{\cos{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}}\right)^{3} + 3 \left(\frac{\cos{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \left(\frac{x \log{\left(\sin{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \operatorname{asin}{\left(x \right)} - \frac{\cos^{2}{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{\sqrt{1 - x^{2}} \sin{\left(x \right)}}\right) + \frac{2 \cos{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{3}{\sqrt{1 - x^{2}}} - \frac{3 \cos^{2}{\left(x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \sin^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}$$