Mister Exam
Other calculators
- 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=4+6x-3x^4
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Derivative of √x+√x+√x
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Derivative of x*e^(-2x)
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Derivative of x+ln(x^2-4)
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Identical expressions
- thx/x
- thx divide by x
Derivative of thx/x
The solution
The first derivative
[src]
2
1 - tanh (x) tanh(x)
------------ - -------
x 2
x
$$\frac{1 - \tanh^{2}{\left(x \right)}}{x} - \frac{\tanh{\left(x \right)}}{x^{2}}$$
The second derivative
[src]
/ 2 \
|-1 + tanh (x) tanh(x) / 2 \ |
2*|------------- + ------- + \-1 + tanh (x)/*tanh(x)|
| x 2 |
\ x /
-----------------------------------------------------
x
$$\frac{2 \left(\left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)} + \frac{\tanh^{2}{\left(x \right)} - 1}{x} + \frac{\tanh{\left(x \right)}}{x^{2}}\right)}{x}$$
The third derivative
[src]
/ / 2 \ / 2 \ \
|/ 2 \ / 2 \ 3*tanh(x) 3*\-1 + tanh (x)/ 3*\-1 + tanh (x)/*tanh(x)|
-2*|\-1 + tanh (x)/*\-1 + 3*tanh (x)/ + --------- + ----------------- + -------------------------|
| 3 2 x |
\ x x /
--------------------------------------------------------------------------------------------------
x
$$- \frac{2 \left(\left(\tanh^{2}{\left(x \right)} - 1\right) \left(3 \tanh^{2}{\left(x \right)} - 1\right) + \frac{3 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)}}{x} + \frac{3 \left(\tanh^{2}{\left(x \right)} - 1\right)}{x^{2}} + \frac{3 \tanh{\left(x \right)}}{x^{3}}\right)}{x}$$