Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of 3x^2-5x+5
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Derivative of (2*x-1)^2
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Derivative of 2*x^3-3*x^2+6*x+1
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Derivative of (2x+3)^2
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Identical expressions
- e^arctg(sqrt(4x- one))
- e to the power of arctg( square root of (4x minus 1))
- e to the power of arctg( square root of (4x minus one))
- e^arctg(√(4x-1))
- earctg(sqrt(4x-1))
- earctgsqrt4x-1
- e^arctgsqrt4x-1
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Similar expressions
- e^arctg(sqrt(4x+1))
Derivative of e^arctg(sqrt(4x-1))
The solution
You have entered
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/ _________\ atan\\/ 4*x - 1 / E
$$e^{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}$$
E^atan(sqrt(4*x - 1))
The first derivative
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/ _________\
atan\\/ 4*x - 1 /
e
------------------
_________
2*x*\/ 4*x - 1
$$\frac{e^{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}}{2 x \sqrt{4 x - 1}}$$
The second derivative
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/ __________\
/ 1 1 1 \ atan\\/ -1 + 4*x /
|- ------------- - ---------------- + --------------|*e
| 3/2 __________ 4*x*(-1 + 4*x)|
\ (-1 + 4*x) 2*x*\/ -1 + 4*x /
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x
$$\frac{\left(- \frac{1}{\left(4 x - 1\right)^{\frac{3}{2}}} + \frac{1}{4 x \left(4 x - 1\right)} - \frac{1}{2 x \sqrt{4 x - 1}}\right) e^{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}}{x}$$
The third derivative
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/ __________\
/ 6 1 2 3 3 1 \ atan\\/ -1 + 4*x /
|------------- + --------------- + --------------- - --------------- - --------------- + ------------------|*e
| 5/2 2 __________ 3/2 2 2 2 3/2|
\(-1 + 4*x) x *\/ -1 + 4*x x*(-1 + 4*x) 2*x*(-1 + 4*x) 4*x *(-1 + 4*x) 8*x *(-1 + 4*x) /
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x
$$\frac{\left(\frac{6}{\left(4 x - 1\right)^{\frac{5}{2}}} - \frac{3}{2 x \left(4 x - 1\right)^{2}} + \frac{2}{x \left(4 x - 1\right)^{\frac{3}{2}}} - \frac{3}{4 x^{2} \left(4 x - 1\right)} + \frac{1}{x^{2} \sqrt{4 x - 1}} + \frac{1}{8 x^{2} \left(4 x - 1\right)^{\frac{3}{2}}}\right) e^{\operatorname{atan}{\left(\sqrt{4 x - 1} \right)}}}{x}$$