Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of x^4*sin(x)
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Derivative of 3*x
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Derivative of sin(y)
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Derivative of 1/x²
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Identical expressions
- ln(tanhx^ two)
- ln( hyperbolic tangent of gent of x squared )
- ln( hyperbolic tangent of gent of x to the power of two)
- ln(tanhx2)
- lntanhx2
- ln(tanhx²)
- ln(tanhx to the power of 2)
- lntanhx^2
Derivative of ln(tanhx^2)
The solution
You have entered
[src]
/ 2 \ log\tanh (x)/
$$\log{\left(\tanh^{2}{\left(x \right)} \right)}$$
d / / 2 \\ --\log\tanh (x)// dx
$$\frac{d}{d x} \log{\left(\tanh^{2}{\left(x \right)} \right)}$$
The first derivative
[src]
2 2 - 2*tanh (x) -------------- tanh(x)
$$\frac{- 2 \tanh^{2}{\left(x \right)} + 2}{\tanh{\left(x \right)}}$$
The second derivative
[src]
/ 2\ | / 2 \ | | 2 \-1 + tanh (x)/ | 2*|-2 + 2*tanh (x) - ----------------| | 2 | \ tanh (x) /
$$2 \left(2 \tanh^{2}{\left(x \right)} - \frac{\left(\tanh^{2}{\left(x \right)} - 1\right)^{2}}{\tanh^{2}{\left(x \right)}} - 2\right)$$
The third derivative
[src]
/ 2 \
| / 2 \ / 2 \|
/ 2 \ | \-1 + tanh (x)/ 2*\-1 + tanh (x)/|
4*\-1 + tanh (x)/*|-2*tanh(x) - ---------------- + -----------------|
| 3 tanh(x) |
\ tanh (x) /
$$4 \left(\tanh^{2}{\left(x \right)} - 1\right) \left(- 2 \tanh{\left(x \right)} + \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right)}{\tanh{\left(x \right)}} - \frac{\left(\tanh^{2}{\left(x \right)} - 1\right)^{2}}{\tanh^{3}{\left(x \right)}}\right)$$
The graph