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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of x^(4/5)
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Derivative of x^2+5
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Derivative of x^3-1/5*x^2+2*x-4
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Derivative of |x-1|
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Identical expressions
- arctanx(sinx+ two)
- arc tangent of x( sinus of x plus 2)
- arc tangent of x( sinus of x plus two)
- arctanxsinx+2
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Similar expressions
- arctanx(sinx-2)
Derivative of arctanx(sinx+2)
The solution
You have entered
[src]
atan(x)*(sin(x) + 2)
$$\left(\sin{\left(x \right)} + 2\right) \operatorname{atan}{\left(x \right)}$$
atan(x)*(sin(x) + 2)
The first derivative
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sin(x) + 2
---------- + atan(x)*cos(x)
2
1 + x
$$\cos{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin{\left(x \right)} + 2}{x^{2} + 1}$$
The second derivative
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2*cos(x) 2*x*(2 + sin(x))
-atan(x)*sin(x) + -------- - ----------------
2 2
1 + x / 2\
\1 + x /
$$- \frac{2 x \left(\sin{\left(x \right)} + 2\right)}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x^{2} + 1}$$
The third derivative
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/ 2 \
| 4*x |
2*|-1 + ------|*(2 + sin(x))
| 2|
3*sin(x) 6*x*cos(x) \ 1 + x /
-atan(x)*cos(x) - -------- - ---------- + ----------------------------
2 2 2
1 + x / 2\ / 2\
\1 + x / \1 + x /
$$- \frac{6 x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x^{2} + 1} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \left(\sin{\left(x \right)} + 2\right)}{\left(x^{2} + 1\right)^{2}}$$