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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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of (x^2-2*x)/(3+x^2)
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Derivative of (x+1)^2/(x-1)
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Derivative of sin(x)^(23)
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Derivative of sin(2)
- Equation:
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(sin2x)^cosx
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Identical expressions
- y=(sin2x)^cosx
- y equally ( sinus of 2x) to the power of co sinus of e of x
- y=(sin2x)cosx
- y=sin2xcosx
- y=sin2x^cosx
Derivative of y=(sin2x)^cosx
The solution
You have entered
[src]
cos(x) sin (2*x)
$$\sin^{\cos{\left(x \right)}}{\left(2 x \right)}$$
sin(2*x)^cos(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]
cos(x) / 2*cos(x)*cos(2*x)\
sin (2*x)*|-log(sin(2*x))*sin(x) + -----------------|
\ sin(2*x) /
$$\left(- \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(2 x \right)}$$
The second derivative
[src]
/ 2 2 \
cos(x) |/ 2*cos(x)*cos(2*x)\ 4*cos (2*x)*cos(x) 4*cos(2*x)*sin(x)|
sin (2*x)*||log(sin(2*x))*sin(x) - -----------------| - 4*cos(x) - cos(x)*log(sin(2*x)) - ------------------ - -----------------|
|\ sin(2*x) / 2 sin(2*x) |
\ sin (2*x) /
$$\left(\left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right)^{2} - \log{\left(\sin{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{4 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - 4 \cos{\left(x \right)} - \frac{4 \cos{\left(x \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(2 x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 2 3 \
cos(x) | / 2*cos(x)*cos(2*x)\ / 2*cos(x)*cos(2*x)\ | 4*cos (2*x)*cos(x) 4*cos(2*x)*sin(x)| 10*cos(x)*cos(2*x) 12*cos (2*x)*sin(x) 16*cos (2*x)*cos(x)|
sin (2*x)*|- |log(sin(2*x))*sin(x) - -----------------| + 12*sin(x) + log(sin(2*x))*sin(x) + 3*|log(sin(2*x))*sin(x) - -----------------|*|4*cos(x) + cos(x)*log(sin(2*x)) + ------------------ + -----------------| + ------------------ + ------------------- + -------------------|
| \ sin(2*x) / \ sin(2*x) / | 2 sin(2*x) | sin(2*x) 2 3 |
\ \ sin (2*x) / sin (2*x) sin (2*x) /
$$\left(- \left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right)^{3} + 3 \left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right) \left(\log{\left(\sin{\left(2 x \right)} \right)} \cos{\left(x \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + 4 \cos{\left(x \right)} + \frac{4 \cos{\left(x \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) + \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(x \right)} + 12 \sin{\left(x \right)} + \frac{12 \sin{\left(x \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} + \frac{10 \cos{\left(x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{16 \cos{\left(x \right)} \cos^{3}{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(2 x \right)}$$
The graph