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- Derivative of:
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Derivative of -cos(x)
- Derivative of -4
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Identical expressions
- x^(x^ two +3x)
- x to the power of (x squared plus 3x)
- x to the power of (x to the power of two plus 3x)
- x(x2+3x)
- xx2+3x
- x^(x²+3x)
- x to the power of (x to the power of 2+3x)
- x^x^2+3x
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Similar expressions
- x^(x^2-3x)
Derivative of x^(x^2+3x)
The solution
You have entered
[src]
2 x + 3*x x
$$x^{x^{2} + 3 x}$$
/ 2 \ d | x + 3*x| --\x / dx
$$\frac{d}{d x} x^{x^{2} + 3 x}$$
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
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Now simplify:
The answer is:
The first derivative
[src]
2 / 2 \
x + 3*x |x + 3*x |
x *|-------- + (3 + 2*x)*log(x)|
\ x /
$$x^{x^{2} + 3 x} \left(\left(2 x + 3\right) \log{\left(x \right)} + \frac{x^{2} + 3 x}{x}\right)$$
The second derivative
[src]
x*(3 + x) / 2 3 + x 2*(3 + 2*x)\
x *|(3 + x + (3 + 2*x)*log(x)) + 2*log(x) - ----- + -----------|
\ x x /
$$x^{x \left(x + 3\right)} \left(\left(\left(2 x + 3\right) \log{\left(x \right)} + x + 3\right)^{2} + 2 \log{\left(x \right)} - \frac{x + 3}{x} + \frac{2 \cdot \left(2 x + 3\right)}{x}\right)$$
The third derivative
[src]
/ 3*(3 + 2*x) 2*(3 + x) \
| 6 - ----------- + --------- |
x*(3 + x) | 3 x x / 3 + x 2*(3 + 2*x)\|
x *|(3 + x + (3 + 2*x)*log(x)) + --------------------------- + 3*(3 + x + (3 + 2*x)*log(x))*|2*log(x) - ----- + -----------||
\ x \ x x //
$$x^{x \left(x + 3\right)} \left(\left(\left(2 x + 3\right) \log{\left(x \right)} + x + 3\right)^{3} + 3 \left(\left(2 x + 3\right) \log{\left(x \right)} + x + 3\right) \left(2 \log{\left(x \right)} - \frac{x + 3}{x} + \frac{2 \cdot \left(2 x + 3\right)}{x}\right) + \frac{6 + \frac{2 \left(x + 3\right)}{x} - \frac{3 \cdot \left(2 x + 3\right)}{x}}{x}\right)$$
The graph