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How to use it?
- Derivative of:
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Derivative of -2x/(1+x^2)^2
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Derivative of (x^2+49)/x
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Derivative of 2*x-x^2
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Derivative of x*e^x-e^x
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Identical expressions
- (ln(tan(x)^ two + one)- two tanx*atan(tanx)-ln(e^(two x+ two)+ one)+2*e^(x+ one)*atan(e^(x+ one)))/2
- (ln( tangent of (x) squared plus 1) minus 2 tangent of x multiply by arc tangent of gent of ( tangent of x) minus ln(e to the power of (2x plus 2) plus 1) plus 2 multiply by e to the power of (x plus 1) multiply by arc tangent of gent of (e to the power of (x plus 1))) divide by 2
- (ln( tangent of (x) to the power of two plus one) minus two tangent of x multiply by arc tangent of gent of ( tangent of x) minus ln(e to the power of (two x plus two) plus one) plus 2 multiply by e to the power of (x plus one) multiply by arc tangent of gent of (e to the power of (x plus one))) divide by 2
- (ln(tan(x)2+1)-2tanx*atan(tanx)-ln(e(2x+2)+1)+2*e(x+1)*atan(e(x+1)))/2
- lntanx2+1-2tanx*atantanx-lne2x+2+1+2*ex+1*atanex+1/2
- (ln(tan(x)²+1)-2tanx*atan(tanx)-ln(e^(2x+2)+1)+2*e^(x+1)*atan(e^(x+1)))/2
- (ln(tan(x) to the power of 2+1)-2tanx*atan(tanx)-ln(e to the power of (2x+2)+1)+2*e to the power of (x+1)*atan(e to the power of (x+1)))/2
- (ln(tan(x)^2+1)-2tanxatan(tanx)-ln(e^(2x+2)+1)+2e^(x+1)atan(e^(x+1)))/2
- (ln(tan(x)2+1)-2tanxatan(tanx)-ln(e(2x+2)+1)+2e(x+1)atan(e(x+1)))/2
- lntanx2+1-2tanxatantanx-lne2x+2+1+2ex+1atanex+1/2
- lntanx^2+1-2tanxatantanx-lne^2x+2+1+2e^x+1atane^x+1/2
- (ln(tan(x)^2+1)-2tanx*atan(tanx)-ln(e^(2x+2)+1)+2*e^(x+1)*atan(e^(x+1))) divide by 2
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Similar expressions
- (ln(tan(x)^2+1)-2tanx*atan(tanx)+ln(e^(2x+2)+1)+2*e^(x+1)*atan(e^(x+1)))/2
- (ln(tan(x)^2+1)-2tanx*atan(tanx)-ln(e^(2x+2)-1)+2*e^(x+1)*atan(e^(x+1)))/2
- (ln(tan(x)^2-1)-2tanx*atan(tanx)-ln(e^(2x+2)+1)+2*e^(x+1)*atan(e^(x+1)))/2
- (ln(tan(x)^2+1)-2tanx*atan(tanx)-ln(e^(2x-2)+1)+2*e^(x+1)*atan(e^(x+1)))/2
- (ln(tan(x)^2+1)-2tanx*atan(tanx)-ln(e^(2x+2)+1)-2*e^(x+1)*atan(e^(x+1)))/2
- (ln(tan(x)^2+1)-2tanx*atan(tanx)-ln(e^(2x+2)+1)+2*e^(x-1)*atan(e^(x+1)))/2
- (ln(tan(x)^2+1)-2tanx*atan(tanx)-ln(e^(2x+2)+1)+2*e^(x+1)*atan(e^(x-1)))/2
- (ln(tan(x)^2+1)+2tanx*atan(tanx)-ln(e^(2x+2)+1)+2*e^(x+1)*atan(e^(x+1)))/2
- (ln(tan(x)^2+1)-2tanx*arctan(tanx)-ln(e^(2x+2)+1)+2*e^(x+1)*arctan(e^(x+1)))/2
The derivative of the function/
(ln(tan(x)^2+1)-2tanx*atan(tanx)-ln(e^(2x+2)+1)+2*e^(x+1)*atan(e^(x+1)))/2
Derivative of (ln(tan(x)^2+1)-2tanx*atan(tanx)-ln(e^(2x+2)+1)+2*e^(x+1)*atan(e^(x+1)))/2
The solution
You have entered
[src]
/ 2 \ / 2*x + 2 \ x + 1 / x + 1\
log\tan (x) + 1/ - 2*tan(x)*atan(tan(x)) - log\E + 1/ + 2*E *atan\E /
------------------------------------------------------------------------------------
2
$$\frac{2 e^{x + 1} \operatorname{atan}{\left(e^{x + 1} \right)} + \left(\left(\log{\left(\tan^{2}{\left(x \right)} + 1 \right)} - 2 \tan{\left(x \right)} \operatorname{atan}{\left(\tan{\left(x \right)} \right)}\right) - \log{\left(e^{2 x + 2} + 1 \right)}\right)}{2}$$
(log(tan(x)^2 + 1) - 2*tan(x)*atan(tan(x)) - log(E^(2*x + 2) + 1) + (2*E^(x + 1))*atan(E^(x + 1)))/2
The first derivative
[src]
2 + 2*x / 2 \ 2*x + 2 / 2 \
e / x + 1\ x + 1 \-2 - 2*tan (x)/*atan(tan(x)) e \2 + 2*tan (x)/*tan(x)
-tan(x) + ------------ + atan\E /*e + ----------------------------- - ------------ + ----------------------
2 + 2*x 2 2*x + 2 / 2 \
1 + e E + 1 2*\tan (x) + 1/
$$\frac{\left(- 2 \tan^{2}{\left(x \right)} - 2\right) \operatorname{atan}{\left(\tan{\left(x \right)} \right)}}{2} + e^{x + 1} \operatorname{atan}{\left(e^{x + 1} \right)} - \tan{\left(x \right)} + \frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} + \frac{e^{2 x + 2}}{e^{2 x + 2} + 1} - \frac{e^{2 x + 2}}{e^{2 x + 2} + 1}$$
The second derivative
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2 + 2*x
2 e / 1 + x\ 1 + x / 2 \
-1 - tan (x) + -------------- + atan\e /*e - 2*\1 + tan (x)/*atan(tan(x))*tan(x)
2*(1 + x)
1 + e
$$- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{atan}{\left(\tan{\left(x \right)} \right)} + e^{x + 1} \operatorname{atan}{\left(e^{x + 1} \right)} - \tan^{2}{\left(x \right)} - 1 + \frac{e^{2 x + 2}}{e^{2 \left(x + 1\right)} + 1}$$
The third derivative
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2 4 + 4*x 2 + 2*x
/ 1 + x\ 1 + x / 2 \ / 2 \ 2*e 3*e 2 / 2 \
atan\e /*e - 4*\1 + tan (x)/*tan(x) - 2*\1 + tan (x)/ *atan(tan(x)) - ----------------- + -------------- - 4*tan (x)*\1 + tan (x)/*atan(tan(x))
2 2*(1 + x)
/ 2*(1 + x)\ 1 + e
\1 + e /
$$- 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(\tan{\left(x \right)} \right)} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} \operatorname{atan}{\left(\tan{\left(x \right)} \right)} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + e^{x + 1} \operatorname{atan}{\left(e^{x + 1} \right)} + \frac{3 e^{2 x + 2}}{e^{2 \left(x + 1\right)} + 1} - \frac{2 e^{4 x + 4}}{\left(e^{2 \left(x + 1\right)} + 1\right)^{2}}$$