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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of sin(x)^2
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Derivative of cos(x)*x^3
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Derivative of 5/(2x+1)
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Derivative of (-5x+11)^4
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Identical expressions
- sech⁻¹2x+sinh⁻¹x²
- sech⁻¹2x plus hyperbolic sinus of e of ⁻¹x²
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Similar expressions
- sech⁻¹2x-sinh⁻¹x²
Derivative of sech⁻¹2x+sinh⁻¹x²
The solution
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12 1 sech (x) + sinh (x)
$$\sinh^{1}{\left(x \right)} + \operatorname{sech}^{12}{\left(x \right)}$$
sech(x)^12 + sinh(x)^1
The first derivative
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12 - 12*sech (x)*tanh(x) + cosh(x)
$$\cosh{\left(x \right)} - 12 \tanh{\left(x \right)} \operatorname{sech}^{12}{\left(x \right)}$$
The second derivative
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12 / 2 \ 12 2 12*sech (x)*\-1 + tanh (x)/ + 144*sech (x)*tanh (x) + sinh(x)
$$12 \left(\tanh^{2}{\left(x \right)} - 1\right) \operatorname{sech}^{12}{\left(x \right)} + \sinh{\left(x \right)} + 144 \tanh^{2}{\left(x \right)} \operatorname{sech}^{12}{\left(x \right)}$$
The third derivative
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12 3 12 / 2 \ - 1728*sech (x)*tanh (x) - 456*sech (x)*\-1 + tanh (x)/*tanh(x) + cosh(x)
$$- 456 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)} \operatorname{sech}^{12}{\left(x \right)} + \cosh{\left(x \right)} - 1728 \tanh^{3}{\left(x \right)} \operatorname{sech}^{12}{\left(x \right)}$$