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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of (x^5+1)
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Derivative of x^sqrt(x)
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Derivative of log(x+2)
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Derivative of ex^2
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Identical expressions
- arctg(3x)/cos^3x+2x
- arctg(3x) divide by co sinus of e of cubed x plus 2x
- arctg(3x)/cos3x+2x
- arctg3x/cos3x+2x
- arctg(3x)/cos³x+2x
- arctg(3x)/cos to the power of 3x+2x
- arctg3x/cos^3x+2x
- arctg(3x) divide by cos^3x+2x
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Similar expressions
- arctg(3x)/cos^3x-2x
Derivative of arctg(3x)/cos^3x+2x
The solution
You have entered
[src]
atan(3*x)
--------- + 2*x
3
cos (x)
$$2 x + \frac{\operatorname{atan}{\left(3 x \right)}}{\cos^{3}{\left(x \right)}}$$
atan(3*x)/cos(x)^3 + 2*x
The first derivative
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3 3*atan(3*x)*sin(x)
2 + ------------------ + ------------------
/ 2\ 3 4
\1 + 9*x /*cos (x) cos (x)
$$\frac{3 \sin{\left(x \right)} \operatorname{atan}{\left(3 x \right)}}{\cos^{4}{\left(x \right)}} + 2 + \frac{3}{\left(9 x^{2} + 1\right) \cos^{3}{\left(x \right)}}$$
The second derivative
[src]
/ 2 \
| 18*x 4*sin (x)*atan(3*x) 6*sin(x) |
3*|- ----------- + ------------------- + ----------------- + atan(3*x)|
| 2 2 / 2\ |
| / 2\ cos (x) \1 + 9*x /*cos(x) |
\ \1 + 9*x / /
-----------------------------------------------------------------------
3
cos (x)
$$\frac{3 \left(- \frac{18 x}{\left(9 x^{2} + 1\right)^{2}} + \frac{4 \sin^{2}{\left(x \right)} \operatorname{atan}{\left(3 x \right)}}{\cos^{2}{\left(x \right)}} + \operatorname{atan}{\left(3 x \right)} + \frac{6 \sin{\left(x \right)}}{\left(9 x^{2} + 1\right) \cos{\left(x \right)}}\right)}{\cos^{3}{\left(x \right)}}$$
The third derivative
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/ 2 3 2 \
| 18 9 648*x 11*atan(3*x)*sin(x) 20*sin (x)*atan(3*x) 36*sin (x) 162*x*sin(x) |
3*|- ----------- + -------- + ----------- + ------------------- + -------------------- + ------------------ - ------------------|
| 2 2 3 cos(x) 3 / 2\ 2 2 |
| / 2\ 1 + 9*x / 2\ cos (x) \1 + 9*x /*cos (x) / 2\ |
\ \1 + 9*x / \1 + 9*x / \1 + 9*x / *cos(x)/
---------------------------------------------------------------------------------------------------------------------------------
3
cos (x)
$$\frac{3 \left(\frac{648 x^{2}}{\left(9 x^{2} + 1\right)^{3}} - \frac{162 x \sin{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \cos{\left(x \right)}} + \frac{20 \sin^{3}{\left(x \right)} \operatorname{atan}{\left(3 x \right)}}{\cos^{3}{\left(x \right)}} + \frac{11 \sin{\left(x \right)} \operatorname{atan}{\left(3 x \right)}}{\cos{\left(x \right)}} + \frac{36 \sin^{2}{\left(x \right)}}{\left(9 x^{2} + 1\right) \cos^{2}{\left(x \right)}} + \frac{9}{9 x^{2} + 1} - \frac{18}{\left(9 x^{2} + 1\right)^{2}}\right)}{\cos^{3}{\left(x \right)}}$$