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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 x^(7/6)
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Derivative of sec2x
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Derivative of f(x)=2x+3
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Derivative of e^x-7
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Identical expressions
- (x^ two +5x- two)arctg(sqrt(2x))
- (x squared plus 5x minus 2)arctg( square root of (2x))
- (x to the power of two plus 5x minus two)arctg( square root of (2x))
- (x^2+5x-2)arctg(√(2x))
- (x2+5x-2)arctg(sqrt(2x))
- x2+5x-2arctgsqrt2x
- (x²+5x-2)arctg(sqrt(2x))
- (x to the power of 2+5x-2)arctg(sqrt(2x))
- x^2+5x-2arctgsqrt2x
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Similar expressions
- (x^2-5x-2)arctg(sqrt(2x))
- (x^2+5x+2)arctg(sqrt(2x))
Derivative of (x^2+5x-2)arctg(sqrt(2x))
The solution
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[src]
/ 2 \ / _____\ \x + 5*x - 2/*atan\\/ 2*x /
$$\left(x^{2} + 5 x - 2\right) \operatorname{atan}{\left(\sqrt{2 x} \right)}$$
d // 2 \ / _____\\ --\\x + 5*x - 2/*atan\\/ 2*x // dx
$$\frac{d}{d x} \left(x^{2} + 5 x - 2\right) \operatorname{atan}{\left(\sqrt{2 x} \right)}$$
The first derivative
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___ / 2 \
/ _____\ \/ 2 *\x + 5*x - 2/
(5 + 2*x)*atan\\/ 2*x / + --------------------
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2*\/ x *(1 + 2*x)
$$\left(2 x + 5\right) \operatorname{atan}{\left(\sqrt{2 x} \right)} + \frac{\sqrt{2} \left(x^{2} + 5 x - 2\right)}{2 \sqrt{x} \left(2 x + 1\right)}$$
The second derivative
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___ /1 4 \ / 2 \
___ \/ 2 *|- + -------|*\-2 + x + 5*x/
/ _____\ \/ 2 *(5 + 2*x) \x 1 + 2*x/
2*atan\\/ 2*x / + --------------- - -----------------------------------
___ ___
\/ x *(1 + 2*x) 4*\/ x *(1 + 2*x)
$$2 \operatorname{atan}{\left(\sqrt{2 x} \right)} + \frac{\sqrt{2} \cdot \left(2 x + 5\right)}{\sqrt{x} \left(2 x + 1\right)} - \frac{\sqrt{2} \cdot \left(\frac{4}{2 x + 1} + \frac{1}{x}\right) \left(x^{2} + 5 x - 2\right)}{4 \sqrt{x} \left(2 x + 1\right)}$$
The third derivative
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/ / 2 \ /3 32 8 \\
| /1 4 \ \-2 + x + 5*x/*|-- + ---------- + -----------||
| 3*(5 + 2*x)*|- + -------| | 2 2 x*(1 + 2*x)||
___ | \x 1 + 2*x/ \x (1 + 2*x) /|
\/ 2 *|3 - ------------------------- + -----------------------------------------------|
\ 4 8 /
---------------------------------------------------------------------------------------
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\/ x *(1 + 2*x)
$$\frac{\sqrt{2} \left(- \frac{3 \cdot \left(2 x + 5\right) \left(\frac{4}{2 x + 1} + \frac{1}{x}\right)}{4} + \frac{\left(x^{2} + 5 x - 2\right) \left(\frac{32}{\left(2 x + 1\right)^{2}} + \frac{8}{x \left(2 x + 1\right)} + \frac{3}{x^{2}}\right)}{8} + 3\right)}{\sqrt{x} \left(2 x + 1\right)}$$
The graph