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
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of (5*x-6)*cos(x)-5*sin(x)-8
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Derivative of 2/x²
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Derivative of 2/(x+1)^2
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Derivative of 2^(3*x)/3^(2*x)
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Identical expressions
- (sin(2x))^cos(three *x)
- ( sinus of (2x)) to the power of co sinus of e of (3 multiply by x)
- ( sinus of (2x)) to the power of co sinus of e of (three multiply by x)
- (sin(2x))cos(3*x)
- sin2xcos3*x
- (sin(2x))^cos(3x)
- (sin(2x))cos(3x)
- sin2xcos3x
- sin2x^cos3x
Derivative of (sin(2x))^cos(3*x)
The solution
You have entered
[src]
cos(3*x) sin (2*x)
$$\sin^{\cos{\left(3 x \right)}}{\left(2 x \right)}$$
sin(2*x)^cos(3*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(3*x) / 2*cos(2*x)*cos(3*x)\
sin (2*x)*|-3*log(sin(2*x))*sin(3*x) + -------------------|
\ sin(2*x) /
$$\left(- 3 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} + \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) \sin^{\cos{\left(3 x \right)}}{\left(2 x \right)}$$
The second derivative
[src]
/ 2 2 \
cos(3*x) |/ 2*cos(2*x)*cos(3*x)\ 12*cos(2*x)*sin(3*x) 4*cos (2*x)*cos(3*x)|
sin (2*x)*||3*log(sin(2*x))*sin(3*x) - -------------------| - 4*cos(3*x) - 9*cos(3*x)*log(sin(2*x)) - -------------------- - --------------------|
|\ sin(2*x) / sin(2*x) 2 |
\ sin (2*x) /
$$\left(\left(3 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} - \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)^{2} - 9 \log{\left(\sin{\left(2 x \right)} \right)} \cos{\left(3 x \right)} - 4 \cos{\left(3 x \right)} - \frac{12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{4 \cos^{2}{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \sin^{\cos{\left(3 x \right)}}{\left(2 x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 3 2 \
cos(3*x) | / 2*cos(2*x)*cos(3*x)\ / 2*cos(2*x)*cos(3*x)\ | 4*cos (2*x)*cos(3*x) 12*cos(2*x)*sin(3*x)| 38*cos(2*x)*cos(3*x) 16*cos (2*x)*cos(3*x) 36*cos (2*x)*sin(3*x)|
sin (2*x)*|- |3*log(sin(2*x))*sin(3*x) - -------------------| + 36*sin(3*x) + 3*|3*log(sin(2*x))*sin(3*x) - -------------------|*|4*cos(3*x) + 9*cos(3*x)*log(sin(2*x)) + -------------------- + --------------------| + 27*log(sin(2*x))*sin(3*x) - -------------------- + --------------------- + ---------------------|
| \ sin(2*x) / \ sin(2*x) / | 2 sin(2*x) | sin(2*x) 3 2 |
\ \ sin (2*x) / sin (2*x) sin (2*x) /
$$\left(- \left(3 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} - \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)^{3} + 3 \left(3 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} - \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) \left(9 \log{\left(\sin{\left(2 x \right)} \right)} \cos{\left(3 x \right)} + 4 \cos{\left(3 x \right)} + \frac{12 \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{4 \cos^{2}{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) + 27 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(3 x \right)} + 36 \sin{\left(3 x \right)} - \frac{38 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin{\left(2 x \right)}} + \frac{36 \sin{\left(3 x \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} + \frac{16 \cos^{3}{\left(2 x \right)} \cos{\left(3 x \right)}}{\sin^{3}{\left(2 x \right)}}\right) \sin^{\cos{\left(3 x \right)}}{\left(2 x \right)}$$