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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- 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 x^x-1
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Derivative of (x-3)/(x+3)
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Identical expressions
- (x+ one)^(two /x)
- (x plus 1) to the power of (2 divide by x)
- (x plus one) to the power of (two divide by x)
- (x+1)(2/x)
- x+12/x
- x+1^2/x
- (x+1)^(2 divide by x)
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Similar expressions
- (x-1)^(2/x)
Derivative of (x+1)^(2/x)
The solution
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
2
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x / 2*log(x + 1) 2 \
(x + 1) *|- ------------ + ---------|
| 2 x*(x + 1)|
\ x /
$$\left(x + 1\right)^{\frac{2}{x}} \left(\frac{2}{x \left(x + 1\right)} - \frac{2 \log{\left(x + 1 \right)}}{x^{2}}\right)$$
The second derivative
[src]
/ 2 \
2 | / 1 log(1 + x)\ |
- | 2*|----- - ----------| |
x | 1 2 \1 + x x / 2*log(1 + x)|
2*(1 + x) *|- -------- - --------- + ----------------------- + ------------|
| 2 x*(1 + x) x 2 |
\ (1 + x) x /
----------------------------------------------------------------------------
x
$$\frac{2 \left(x + 1\right)^{\frac{2}{x}} \left(- \frac{1}{\left(x + 1\right)^{2}} + \frac{2 \left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right)^{2}}{x} - \frac{2}{x \left(x + 1\right)} + \frac{2 \log{\left(x + 1 \right)}}{x^{2}}\right)}{x}$$
The third derivative
[src]
/ 3 / 1 log(1 + x)\ / 1 2*log(1 + x) 2 \\
2 | / 1 log(1 + x)\ 6*|----- - ----------|*|-------- - ------------ + ---------||
- | 4*|----- - ----------| \1 + x x / | 2 2 x*(1 + x)||
x | 2 6*log(1 + x) 3 \1 + x x / 6 \(1 + x) x /|
2*(1 + x) *|-------- - ------------ + ---------- + ----------------------- + ---------- - ------------------------------------------------------------|
| 3 3 2 2 2 x |
\(1 + x) x x*(1 + x) x x *(1 + x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{2 \left(x + 1\right)^{\frac{2}{x}} \left(\frac{2}{\left(x + 1\right)^{3}} - \frac{6 \left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{2}{x \left(x + 1\right)} - \frac{2 \log{\left(x + 1 \right)}}{x^{2}}\right)}{x} + \frac{3}{x \left(x + 1\right)^{2}} + \frac{4 \left(\frac{1}{x + 1} - \frac{\log{\left(x + 1 \right)}}{x}\right)^{3}}{x^{2}} + \frac{6}{x^{2} \left(x + 1\right)} - \frac{6 \log{\left(x + 1 \right)}}{x^{3}}\right)}{x}$$
The graph