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- 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 (x+x^2)^x
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Derivative of -sin(x)+cos(x)
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Derivative of sin(x)-2*x
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Derivative of f(x)=1/3x²+x²+2x
- Limit of the function:
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(x+x^2)^x
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Identical expressions
- (x+x^ two)^x
- (x plus x squared ) to the power of x
- (x plus x to the power of two) to the power of x
- (x+x2)x
- x+x2x
- (x+x²)^x
- (x+x to the power of 2) to the power of x
- x+x^2^x
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Similar expressions
- (x-x^2)^x
Derivative of (x+x^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]
x
/ 2\ /x*(1 + 2*x) / 2\\
\x + x / *|----------- + log\x + x /|
| 2 |
\ x + x /
$$\left(x^{2} + x\right)^{x} \left(\frac{x \left(2 x + 1\right)}{x^{2} + x} + \log{\left(x^{2} + x \right)}\right)$$
The second derivative
[src]
/ 2\
| 2*(1 + 2*x) (1 + 2*x) |
| 2 2 + ----------- - ----------|
x |/1 + 2*x \ x x*(1 + x) |
(x*(1 + x)) *||------- + log(x*(1 + x))| + ----------------------------|
\\ 1 + x / 1 + x /
$$\left(x \left(x + 1\right)\right)^{x} \left(\left(\log{\left(x \left(x + 1\right) \right)} + \frac{2 x + 1}{x + 1}\right)^{2} + \frac{2 + \frac{2 \left(2 x + 1\right)}{x} - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}}{x + 1}\right)$$
The third derivative
[src]
/ 2 3 \
| 6*(1 + 2*x) 3*(1 + 2*x) 2*(1 + 2*x) / 2\|
| 6 - ----------- - ------------ + ------------ /1 + 2*x \ | 2*(1 + 2*x) (1 + 2*x) ||
| 3 1 + x x*(1 + x) 2 3*|------- + log(x*(1 + x))|*|2 + ----------- - ----------||
x |/1 + 2*x \ x*(1 + x) \ 1 + x / \ x x*(1 + x) /|
(x*(1 + x)) *||------- + log(x*(1 + x))| + --------------------------------------------- + -----------------------------------------------------------|
\\ 1 + x / x*(1 + x) 1 + x /
$$\left(x \left(x + 1\right)\right)^{x} \left(\left(\log{\left(x \left(x + 1\right) \right)} + \frac{2 x + 1}{x + 1}\right)^{3} + \frac{3 \left(\log{\left(x \left(x + 1\right) \right)} + \frac{2 x + 1}{x + 1}\right) \left(2 + \frac{2 \left(2 x + 1\right)}{x} - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}\right)}{x + 1} + \frac{6 - \frac{6 \left(2 x + 1\right)}{x + 1} - \frac{3 \left(2 x + 1\right)^{2}}{x \left(x + 1\right)} + \frac{2 \left(2 x + 1\right)^{3}}{x \left(x + 1\right)^{2}}}{x \left(x + 1\right)}\right)$$
The graph