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+49)/x
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Derivative of sec2x
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Derivative of x*e^x-e^x
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Derivative of (x-3)/sqrt(x)
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Identical expressions
- cos(three *x)^sin(four *x)
- co sinus of e of (3 multiply by x) to the power of sinus of (4 multiply by x)
- co sinus of e of (three multiply by x) to the power of sinus of (four multiply by x)
- cos(3*x)sin(4*x)
- cos3*xsin4*x
- cos(3x)^sin(4x)
- cos(3x)sin(4x)
- cos3xsin4x
- cos3x^sin4x
Derivative of cos(3*x)^sin(4*x)
The solution
You have entered
[src]
sin(4*x) cos (3*x)
$$\cos^{\sin{\left(4 x \right)}}{\left(3 x \right)}$$
cos(3*x)^sin(4*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]
sin(4*x) / 3*sin(3*x)*sin(4*x)\
cos (3*x)*|4*cos(4*x)*log(cos(3*x)) - -------------------|
\ cos(3*x) /
$$\left(4 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(4 x \right)} - \frac{3 \sin{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos{\left(3 x \right)}}\right) \cos^{\sin{\left(4 x \right)}}{\left(3 x \right)}$$
The second derivative
[src]
/ 2 2 \
sin(4*x) |/ 3*sin(3*x)*sin(4*x)\ 24*cos(4*x)*sin(3*x) 9*sin (3*x)*sin(4*x)|
cos (3*x)*||4*cos(4*x)*log(cos(3*x)) - -------------------| - 9*sin(4*x) - 16*log(cos(3*x))*sin(4*x) - -------------------- - --------------------|
|\ cos(3*x) / cos(3*x) 2 |
\ cos (3*x) /
$$\left(\left(4 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(4 x \right)} - \frac{3 \sin{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos{\left(3 x \right)}}\right)^{2} - 16 \log{\left(\cos{\left(3 x \right)} \right)} \sin{\left(4 x \right)} - \frac{9 \sin^{2}{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos^{2}{\left(3 x \right)}} - \frac{24 \sin{\left(3 x \right)} \cos{\left(4 x \right)}}{\cos{\left(3 x \right)}} - 9 \sin{\left(4 x \right)}\right) \cos^{\sin{\left(4 x \right)}}{\left(3 x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 2 3 \
sin(4*x) |/ 3*sin(3*x)*sin(4*x)\ / 3*sin(3*x)*sin(4*x)\ | 9*sin (3*x)*sin(4*x) 24*cos(4*x)*sin(3*x)| 108*sin (3*x)*cos(4*x) 54*sin (3*x)*sin(4*x) 90*sin(3*x)*sin(4*x)|
cos (3*x)*||4*cos(4*x)*log(cos(3*x)) - -------------------| - 108*cos(4*x) - 64*cos(4*x)*log(cos(3*x)) - 3*|4*cos(4*x)*log(cos(3*x)) - -------------------|*|9*sin(4*x) + 16*log(cos(3*x))*sin(4*x) + -------------------- + --------------------| - ---------------------- - --------------------- + --------------------|
|\ cos(3*x) / \ cos(3*x) / | 2 cos(3*x) | 2 3 cos(3*x) |
\ \ cos (3*x) / cos (3*x) cos (3*x) /
$$\left(\left(4 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(4 x \right)} - \frac{3 \sin{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos{\left(3 x \right)}}\right)^{3} - 3 \left(4 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(4 x \right)} - \frac{3 \sin{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos{\left(3 x \right)}}\right) \left(16 \log{\left(\cos{\left(3 x \right)} \right)} \sin{\left(4 x \right)} + \frac{9 \sin^{2}{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos^{2}{\left(3 x \right)}} + \frac{24 \sin{\left(3 x \right)} \cos{\left(4 x \right)}}{\cos{\left(3 x \right)}} + 9 \sin{\left(4 x \right)}\right) - 64 \log{\left(\cos{\left(3 x \right)} \right)} \cos{\left(4 x \right)} - \frac{54 \sin^{3}{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos^{3}{\left(3 x \right)}} - \frac{108 \sin^{2}{\left(3 x \right)} \cos{\left(4 x \right)}}{\cos^{2}{\left(3 x \right)}} + \frac{90 \sin{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos{\left(3 x \right)}} - 108 \cos{\left(4 x \right)}\right) \cos^{\sin{\left(4 x \right)}}{\left(3 x \right)}$$