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 y/2
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Derivative of (x+5)/(x-1)
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Derivative of x+9
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Derivative of (x-4)
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Identical expressions
- y=x^(e^ctg(x))
- y equally x to the power of (e to the power of ctg(x))
- y=x(ectg(x))
- y=xectgx
- y=x^e^ctgx
Derivative of y=x^(e^ctg(x))
The solution
You have entered
[src]
/ cot(x)\ \e / x
$$x^{e^{\cot{\left(x \right)}}}$$
/ / cot(x)\\ d | \e /| --\x / dx
$$\frac{d}{d x} x^{e^{\cot{\left(x \right)}}}$$
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]
/ cot(x)\ / cot(x) \
\e / |e / 2 \ cot(x) |
x *|------- + \-1 - cot (x)/*e *log(x)|
\ x /
$$x^{e^{\cot{\left(x \right)}}} \left(\left(- \cot^{2}{\left(x \right)} - 1\right) e^{\cot{\left(x \right)}} \log{\left(x \right)} + \frac{e^{\cot{\left(x \right)}}}{x}\right)$$
The second derivative
[src]
/ cot(x)\ / 2 2 / 2 \ \
\e / | 1 / 2 \ / 1 / 2 \ \ cot(x) 2*\1 + cot (x)/ / 2 \ | cot(x)
x *|- -- + \1 + cot (x)/ *log(x) + |- - + \1 + cot (x)/*log(x)| *e - --------------- + 2*\1 + cot (x)/*cot(x)*log(x)|*e
| 2 \ x / x |
\ x /
$$x^{e^{\cot{\left(x \right)}}} \left(\left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{1}{x}\right)^{2} e^{\cot{\left(x \right)}} + \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot{\left(x \right)} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) e^{\cot{\left(x \right)}}$$
The third derivative
[src]
/ 2 \
/ cot(x)\ | 3 3 / 2 \ / 2 \ 2 / 2 \ / 2 / 2 \ \ 2 |
\e / | 2 / 2 \ / 1 / 2 \ \ 2*cot(x) 3*\1 + cot (x)/ 3*\1 + cot (x)/ / 2 \ 6*\1 + cot (x)/*cot(x) / 1 / 2 \ \ | 1 / 2 \ 2*\1 + cot (x)/ / 2 \ | cot(x) 2 / 2 \ / 2 \ | cot(x)
-x *|- -- + \1 + cot (x)/ *log(x) + |- - + \1 + cot (x)/*log(x)| *e - ---------------- - --------------- + 2*\1 + cot (x)/ *log(x) - ---------------------- + 3*|- - + \1 + cot (x)/*log(x)|*|- -- + \1 + cot (x)/ *log(x) - --------------- + 2*\1 + cot (x)/*cot(x)*log(x)|*e + 4*cot (x)*\1 + cot (x)/*log(x) + 6*\1 + cot (x)/ *cot(x)*log(x)|*e
| 3 \ x / x 2 x \ x / | 2 x | |
\ x x \ x / /
$$- x^{e^{\cot{\left(x \right)}}} \left(\left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{1}{x}\right)^{3} e^{2 \cot{\left(x \right)}} + \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + 6 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} \cot{\left(x \right)} + 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot^{2}{\left(x \right)} + 3 \left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{1}{x}\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot{\left(x \right)} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) e^{\cot{\left(x \right)}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{x} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2}{x^{3}}\right) e^{\cot{\left(x \right)}}$$