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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 e^(x*(-2))
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Derivative of 1/x^5
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Derivative of x^5*cos(x)
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Derivative of x^(3/4)
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Identical expressions
- y=(e⁶*(six ^x))+(sin(x)*arctg(x))
- y equally (e⁶ multiply by (6 to the power of x)) plus ( sinus of (x) multiply by arctg(x))
- y equally (e⁶ multiply by (six to the power of x)) plus ( sinus of (x) multiply by arctg(x))
- y=(e⁶*(6x))+(sin(x)*arctg(x))
- y=e⁶*6x+sinx*arctgx
- y=(e⁶(6^x))+(sin(x)arctg(x))
- y=(e⁶(6x))+(sin(x)arctg(x))
- y=e⁶6x+sinxarctgx
- y=e⁶6^x+sinxarctgx
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Similar expressions
- y=(e⁶*(6^x))-(sin(x)*arctg(x))
- y=(e⁶*(6^x))+(sinx*arctg(x))
Derivative of y=(e⁶*(6^x))+(sin(x)*arctg(x))
The solution
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[src]
6 x E *6 + sin(x)*atan(x)
$$6^{x} e^{6} + \sin{\left(x \right)} \operatorname{atan}{\left(x \right)}$$
E^6*6^x + sin(x)*atan(x)
The first derivative
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sin(x) x 6
------ + atan(x)*cos(x) + 6 *e *log(6)
2
1 + x
$$6^{x} e^{6} \log{\left(6 \right)} + \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin{\left(x \right)}}{x^{2} + 1}$$
The second derivative
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2*cos(x) x 2 6 2*x*sin(x)
-atan(x)*sin(x) + -------- + 6 *log (6)*e - ----------
2 2
1 + x / 2\
\1 + x /
$$6^{x} e^{6} \log{\left(6 \right)}^{2} - \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x^{2} + 1}$$
The third derivative
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2
3*sin(x) 2*sin(x) x 3 6 6*x*cos(x) 8*x *sin(x)
-atan(x)*cos(x) - -------- - --------- + 6 *log (6)*e - ---------- + -----------
2 2 2 3
1 + x / 2\ / 2\ / 2\
\1 + x / \1 + x / \1 + x /
$$6^{x} e^{6} \log{\left(6 \right)}^{3} + \frac{8 x^{2} \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x^{2} + 1} - \frac{2 \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}$$
The graph