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 log6x
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Derivative of y=ln(tanhx)
- Derivative of log_7(12x+5)
- Derivative of sqrt(tan(x))
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Identical expressions
- y=ln(tanhx)
- y equally ln( hyperbolic tangent of gent of x)
- y=lntanhx
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Similar expressions
- ln(tanhx^2)
Derivative of y=ln(tanhx)
The solution
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log(tanh(x))
$$\log{\left(\tanh{\left(x \right)} \right)}$$
d --(log(tanh(x))) dx
$$\frac{d}{d x} \log{\left(\tanh{\left(x \right)} \right)}$$
The first derivative
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2 1 - tanh (x) ------------ tanh(x)
$$\frac{1 - \tanh^{2}{\left(x \right)}}{\tanh{\left(x \right)}}$$
The second derivative
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2
/ 2 \
2 \-1 + tanh (x)/
-2 + 2*tanh (x) - ----------------
2
tanh (x)
$$- \frac{\left(\tanh^{2}{\left(x \right)} - 1\right)^{2}}{\tanh^{2}{\left(x \right)}} + 2 \tanh^{2}{\left(x \right)} - 2$$
The third derivative
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/ 2 \
| / 2 \ / 2 \|
/ 2 \ | \-1 + tanh (x)/ 2*\-1 + tanh (x)/|
2*\-1 + tanh (x)/*|-2*tanh(x) - ---------------- + -----------------|
| 3 tanh(x) |
\ tanh (x) /
$$2 \left(\tanh^{2}{\left(x \right)} - 1\right) \left(- \frac{\left(\tanh^{2}{\left(x \right)} - 1\right)^{2}}{\tanh^{3}{\left(x \right)}} + \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right)}{\tanh{\left(x \right)}} - 2 \tanh{\left(x \right)}\right)$$
The graph