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- Derivative of:
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Derivative of x^12
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Derivative of -e^x
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Derivative of e^(2-x)
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Derivative of x^2-4*x
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Identical expressions
- y=(x- four)^5arcctg(3x^ two)
- y equally (x minus 4) to the power of 5arcctg(3x squared )
- y equally (x minus four) to the power of 5arcctg(3x to the power of two)
- y=(x-4)5arcctg(3x2)
- y=x-45arcctg3x2
- y=(x-4)⁵arcctg(3x²)
- y=(x-4) to the power of 5arcctg(3x to the power of 2)
- y=x-4^5arcctg3x^2
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Similar expressions
- y=(x+4)^5arcctg(3x^2)
Derivative of y=(x-4)^5arcctg(3x^2)
The solution
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[src]
5 / 2\ (x - 4) *acot\3*x /
$$\left(x - 4\right)^{5} \operatorname{acot}{\left(3 x^{2} \right)}$$
(x - 4)^5*acot(3*x^2)
The first derivative
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5
4 / 2\ 6*x*(x - 4)
5*(x - 4) *acot\3*x / - ------------
4
1 + 9*x
$$- \frac{6 x \left(x - 4\right)^{5}}{9 x^{4} + 1} + 5 \left(x - 4\right)^{4} \operatorname{acot}{\left(3 x^{2} \right)}$$
The second derivative
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/ / 4 \\
| 2 | 36*x ||
| 3*(-4 + x) *|-1 + --------||
| | 4||
3 | / 2\ 30*x*(-4 + x) \ 1 + 9*x /|
2*(-4 + x) *|10*acot\3*x / - ------------- + ---------------------------|
| 4 4 |
\ 1 + 9*x 1 + 9*x /
$$2 \left(x - 4\right)^{3} \left(- \frac{30 x \left(x - 4\right)}{9 x^{4} + 1} + \frac{3 \left(x - 4\right)^{2} \left(\frac{36 x^{4}}{9 x^{4} + 1} - 1\right)}{9 x^{4} + 1} + 10 \operatorname{acot}{\left(3 x^{2} \right)}\right)$$
The third derivative
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/ / 4 \ / 4 \\
| 2 | 36*x | 3 3 | 72*x ||
| 15*(-4 + x) *|-1 + --------| 36*x *(-4 + x) *|-5 + --------||
| | 4| | 4||
2 | / 2\ 60*x*(-4 + x) \ 1 + 9*x / \ 1 + 9*x /|
6*(-4 + x) *|10*acot\3*x / - ------------- + ---------------------------- - -------------------------------|
| 4 4 2 |
| 1 + 9*x 1 + 9*x / 4\ |
\ \1 + 9*x / /
$$6 \left(x - 4\right)^{2} \left(- \frac{36 x^{3} \left(x - 4\right)^{3} \left(\frac{72 x^{4}}{9 x^{4} + 1} - 5\right)}{\left(9 x^{4} + 1\right)^{2}} - \frac{60 x \left(x - 4\right)}{9 x^{4} + 1} + \frac{15 \left(x - 4\right)^{2} \left(\frac{36 x^{4}}{9 x^{4} + 1} - 1\right)}{9 x^{4} + 1} + 10 \operatorname{acot}{\left(3 x^{2} \right)}\right)$$
The graph