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- Derivative of:
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Derivative of x^2/e^x
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Derivative of 4*sqrt(3)*x/3
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Derivative of y=(x^3-3)(x^2+4x+1)
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Derivative of x^x-1
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Identical expressions
- y=tanh^ two (x+ one)+sech^ two (x+ one)
- y equally hyperbolic tangent of gent of squared (x plus 1) plus sech squared (x plus 1)
- y equally hyperbolic tangent of gent of to the power of two (x plus one) plus sech to the power of two (x plus one)
- y=tanh2(x+1)+sech2(x+1)
- y=tanh2x+1+sech2x+1
- y=tanh²(x+1)+sech²(x+1)
- y=tanh to the power of 2(x+1)+sech to the power of 2(x+1)
- y=tanh^2x+1+sech^2x+1
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Similar expressions
- y=tanh^2(x-1)+sech^2(x+1)
- y=tanh^2(x+1)-sech^2(x+1)
- y=tanh^2(x+1)+sech^2(x-1)
Derivative of y=tanh^2(x+1)+sech^2(x+1)
The solution
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2 2 tanh (x + 1) + sech (x + 1)
$$\tanh^{2}{\left(x + 1 \right)} + \operatorname{sech}^{2}{\left(x + 1 \right)}$$
d / 2 2 \ --\tanh (x + 1) + sech (x + 1)/ dx
$$\frac{d}{d x} \left(\tanh^{2}{\left(x + 1 \right)} + \operatorname{sech}^{2}{\left(x + 1 \right)}\right)$$
The first derivative
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/ 2 \ 2 \2 - 2*tanh (x + 1)/*tanh(x + 1) - 2*sech (x + 1)*tanh(x + 1)
$$- 2 \tanh{\left(x + 1 \right)} \operatorname{sech}^{2}{\left(x + 1 \right)} + \left(- 2 \tanh^{2}{\left(x + 1 \right)} + 2\right) \tanh{\left(x + 1 \right)}$$
The second derivative
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/ 2 \ |/ 2 \ 2 / 2 \ 2 2 2 / 2 \| 2*\\-1 + tanh (1 + x)/ + sech (1 + x)*\-1 + tanh (1 + x)/ + 2*sech (1 + x)*tanh (1 + x) + 2*tanh (1 + x)*\-1 + tanh (1 + x)//
$$2 \left(2 \tanh^{2}{\left(x + 1 \right)} \operatorname{sech}^{2}{\left(x + 1 \right)} + 2 \left(\tanh^{2}{\left(x + 1 \right)} - 1\right) \tanh^{2}{\left(x + 1 \right)} + \left(\tanh^{2}{\left(x + 1 \right)} - 1\right) \operatorname{sech}^{2}{\left(x + 1 \right)} + \left(\tanh^{2}{\left(x + 1 \right)} - 1\right)^{2}\right)$$
The third derivative
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/ 2 \ | / 2 \ 2 2 2 / 2 \ 2 / 2 \| -8*\2*\-1 + tanh (1 + x)/ + sech (1 + x)*tanh (1 + x) + tanh (1 + x)*\-1 + tanh (1 + x)/ + 2*sech (1 + x)*\-1 + tanh (1 + x)//*tanh(1 + x)
$$- 8 \cdot \left(\tanh^{2}{\left(x + 1 \right)} \operatorname{sech}^{2}{\left(x + 1 \right)} + \left(\tanh^{2}{\left(x + 1 \right)} - 1\right) \tanh^{2}{\left(x + 1 \right)} + 2 \left(\tanh^{2}{\left(x + 1 \right)} - 1\right) \operatorname{sech}^{2}{\left(x + 1 \right)} + 2 \left(\tanh^{2}{\left(x + 1 \right)} - 1\right)^{2}\right) \tanh{\left(x + 1 \right)}$$
The graph