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- Derivative of:
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Derivative of e^-1
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Derivative of 2*x^5
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Derivative of f(x)=1
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Derivative of e^x*x^2
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Identical expressions
- abs(x^ two -14x+ forty-five)
- abs(x squared minus 14x plus 45)
- abs(x to the power of two minus 14x plus forty minus five)
- abs(x2-14x+45)
- absx2-14x+45
- abs(x²-14x+45)
- abs(x to the power of 2-14x+45)
- absx^2-14x+45
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Similar expressions
- abs(x^2+14x+45)
- abs(x^2-14x-45)
Derivative of abs(x^2-14x+45)
The solution
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[src]
| 2 | |x - 14*x + 45|
$$\left|{x^{2} - 14 x + 45}\right|$$
d /| 2 |\ --\|x - 14*x + 45|/ dx
$$\frac{d}{d x} \left|{x^{2} - 14 x + 45}\right|$$
The first derivative
[src]
/ 2 \ (-14 + 2*x)*sign\45 + x - 14*x/
$$\left(2 x - 14\right) \operatorname{sign}{\left(x^{2} - 14 x + 45 \right)}$$
The second derivative
[src]
/ 2 / 2 \ / 2 \\ 2*\4*(-7 + x) *DiracDelta\45 + x - 14*x/ + sign\45 + x - 14*x//
$$2 \cdot \left(4 \left(x - 7\right)^{2} \delta\left(x^{2} - 14 x + 45\right) + \operatorname{sign}{\left(x^{2} - 14 x + 45 \right)}\right)$$
The third derivative
[src]
/ / 2 \ 2 / 2 \\ 8*(-7 + x)*\3*DiracDelta\45 + x - 14*x/ + 2*(-7 + x) *DiracDelta\45 + x - 14*x, 1//
$$8 \left(x - 7\right) \left(2 \left(x - 7\right)^{2} \delta^{\left( 1 \right)}\left( x^{2} - 14 x + 45 \right) + 3 \delta\left(x^{2} - 14 x + 45\right)\right)$$
The graph