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 8^x
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Derivative of 2*sinh(x)*cosh(x)
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Derivative of x^2*asinh(x)*acosh(x)
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Derivative of (x^2-4)/x
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Identical expressions
- cot(three *x)^(two *e^x)
- cotangent of (3 multiply by x) to the power of (2 multiply by e to the power of x)
- cotangent of (three multiply by x) to the power of (two multiply by e to the power of x)
- cot(3*x)(2*ex)
- cot3*x2*ex
- cot(3x)^(2e^x)
- cot(3x)(2ex)
- cot3x2ex
- cot3x^2e^x
Derivative of cot(3*x)^(2*e^x)
The solution
You have entered
[src]
x
2*e
(cot(3*x))
$$\cot^{2 e^{x}}{\left(3 x \right)}$$
/ x\ d | 2*e | --\(cot(3*x)) / dx
$$\frac{d}{d x} \cot^{2 e^{x}}{\left(3 x \right)}$$
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
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Now simplify:
The answer is:
The first derivative
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x / / 2 \ x\
2*e | x 2*\-3 - 3*cot (3*x)/*e |
(cot(3*x)) *|2*e *log(cot(3*x)) + -----------------------|
\ cot(3*x) /
$$\left(2 e^{x} \log{\left(\cot{\left(3 x \right)} \right)} + \frac{2 \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) e^{x}}{\cot{\left(3 x \right)}}\right) \cot^{2 e^{x}}{\left(3 x \right)}$$
The second derivative
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/ 2 2 \
x | / 2 \ / 2 \ / / 2 \\ |
2*e | 2 9*\1 + cot (3*x)/ 6*\1 + cot (3*x)/ | 3*\1 + cot (3*x)/| x | x
2*(cot(3*x)) *|18 + 18*cot (3*x) - ------------------ - ----------------- + 2*|-log(cot(3*x)) + -----------------| *e + log(cot(3*x))|*e
| 2 cot(3*x) \ cot(3*x) / |
\ cot (3*x) /
$$2 \cdot \left(2 \left(- \log{\left(\cot{\left(3 x \right)} \right)} + \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}}\right)^{2} e^{x} + 18 \cot^{2}{\left(3 x \right)} + \log{\left(\cot{\left(3 x \right)} \right)} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 18\right) e^{x} \cot^{2 e^{x}}{\left(3 x \right)}$$
The third derivative
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/ 3 2 3 2 / 2\ \
x | / 2 \ / 2 \ / 2 \ / / 2 \\ / 2 \ / / 2 \\ | / 2 \ / 2 \ | |
2*e | 2 / 2 \ 54*\1 + cot (3*x)/ 27*\1 + cot (3*x)/ 9*\1 + cot (3*x)/ | 3*\1 + cot (3*x)/| 2*x 108*\1 + cot (3*x)/ | 3*\1 + cot (3*x)/| | 2 6*\1 + cot (3*x)/ 9*\1 + cot (3*x)/ | x | x
2*(cot(3*x)) *|54 + 54*cot (3*x) - 108*\1 + cot (3*x)/*cot(3*x) - ------------------- - ------------------- - ----------------- - 4*|-log(cot(3*x)) + -----------------| *e + -------------------- + 6*|-log(cot(3*x)) + -----------------|*|-18 - log(cot(3*x)) - 18*cot (3*x) + ----------------- + ------------------|*e + log(cot(3*x))|*e
| 3 2 cot(3*x) \ cot(3*x) / cot(3*x) \ cot(3*x) / | cot(3*x) 2 | |
\ cot (3*x) cot (3*x) \ cot (3*x) / /
$$2 \left(- 4 \left(- \log{\left(\cot{\left(3 x \right)} \right)} + \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}}\right)^{3} e^{2 x} + 6 \cdot \left(- \log{\left(\cot{\left(3 x \right)} \right)} + \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}}\right) \left(- 18 \cot^{2}{\left(3 x \right)} - \log{\left(\cot{\left(3 x \right)} \right)} + \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} + \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 18\right) e^{x} - 108 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} + 54 \cot^{2}{\left(3 x \right)} + \frac{108 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot{\left(3 x \right)}} + \log{\left(\cot{\left(3 x \right)} \right)} - \frac{54 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3}}{\cot^{3}{\left(3 x \right)}} - \frac{27 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 54\right) e^{x} \cot^{2 e^{x}}{\left(3 x \right)}$$
The graph