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How to use it?
- Derivative of:
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Derivative of 3x-x^2
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Derivative of 3x^2-4x+5
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Derivative of 3*x^2-1/x^3
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Derivative of (3x-1)^2
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Identical expressions
- arctg(one +x^(one / four))^ three
- arctg(1 plus x to the power of (1 divide by 4)) cubed
- arctg(one plus x to the power of (one divide by four)) to the power of three
- arctg(1+x(1/4))3
- arctg1+x1/43
- arctg(1+x^(1/4))³
- arctg(1+x to the power of (1/4)) to the power of 3
- arctg1+x^1/4^3
- arctg(1+x^(1 divide by 4))^3
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Similar expressions
- arctg(1-x^(1/4))^3
Derivative of arctg(1+x^(1/4))^3
The solution
You have entered
[src]
3/ 4 ___\ atan \1 + \/ x /
$$\operatorname{atan}^{3}{\left(\sqrt[4]{x} + 1 \right)}$$
d / 3/ 4 ___\\ --\atan \1 + \/ x // dx
$$\frac{d}{d x} \operatorname{atan}^{3}{\left(\sqrt[4]{x} + 1 \right)}$$
The first derivative
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2/ 4 ___\
3*atan \1 + \/ x /
-------------------------
/ 2\
3/4 | / 4 ___\ |
4*x *\1 + \1 + \/ x / /
$$\frac{3 \operatorname{atan}^{2}{\left(\sqrt[4]{x} + 1 \right)}}{4 x^{\frac{3}{4}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)}$$
The second derivative
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/ / 4 ___\ / 4 ___\ / 4 ___\\
| 3*atan\1 + \/ x / 2 2*\1 + \/ x /*atan\1 + \/ x /| / 4 ___\
3*|- ----------------- + ----------------------- - -----------------------------|*atan\1 + \/ x /
| 7/4 / 2\ / 2\ |
| x 3/2 | / 4 ___\ | 3/2 | / 4 ___\ | |
\ x *\1 + \1 + \/ x / / x *\1 + \1 + \/ x / / /
-------------------------------------------------------------------------------------------------
/ 2\
| / 4 ___\ |
16*\1 + \1 + \/ x / /
$$\frac{3 \left(- \frac{2 \left(\sqrt[4]{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} + 1 \right)}}{x^{\frac{3}{2}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)} + \frac{2}{x^{\frac{3}{2}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(\sqrt[4]{x} + 1 \right)}}{x^{\frac{7}{4}}}\right) \operatorname{atan}{\left(\sqrt[4]{x} + 1 \right)}}{16 \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)}$$
The third derivative
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/ 2 \
| 2/ 4 ___\ / 4 ___\ 2/ 4 ___\ / 4 ___\ / 4 ___\ / 4 ___\ 2/ 4 ___\ 2/ 4 ___\ / 4 ___\|
| 2 21*atan \1 + \/ x / 18*atan\1 + \/ x / 2*atan \1 + \/ x / 12*\1 + \/ x /*atan\1 + \/ x / 8*\1 + \/ x / *atan \1 + \/ x / 18*atan \1 + \/ x /*\1 + \/ x /|
3*|------------------------ + ------------------- - ----------------------- - ----------------------- - ------------------------------ + ------------------------------- + -------------------------------|
| 2 11/4 / 2\ / 2\ 2 2 / 2\ |
| / 2\ x 5/2 | / 4 ___\ | 9/4 | / 4 ___\ | / 2\ / 2\ 5/2 | / 4 ___\ | |
| 9/4 | / 4 ___\ | x *\1 + \1 + \/ x / / x *\1 + \1 + \/ x / / 9/4 | / 4 ___\ | 9/4 | / 4 ___\ | x *\1 + \1 + \/ x / / |
\x *\1 + \1 + \/ x / / x *\1 + \1 + \/ x / / x *\1 + \1 + \/ x / / /
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/ 2\
| / 4 ___\ |
64*\1 + \1 + \/ x / /
$$\frac{3 \cdot \left(\frac{18 \left(\sqrt[4]{x} + 1\right) \operatorname{atan}^{2}{\left(\sqrt[4]{x} + 1 \right)}}{x^{\frac{5}{2}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)} - \frac{18 \operatorname{atan}{\left(\sqrt[4]{x} + 1 \right)}}{x^{\frac{5}{2}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)} + \frac{8 \left(\sqrt[4]{x} + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt[4]{x} + 1 \right)}}{x^{\frac{9}{4}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)^{2}} - \frac{2 \operatorname{atan}^{2}{\left(\sqrt[4]{x} + 1 \right)}}{x^{\frac{9}{4}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)} - \frac{12 \left(\sqrt[4]{x} + 1\right) \operatorname{atan}{\left(\sqrt[4]{x} + 1 \right)}}{x^{\frac{9}{4}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)^{2}} + \frac{21 \operatorname{atan}^{2}{\left(\sqrt[4]{x} + 1 \right)}}{x^{\frac{11}{4}}} + \frac{2}{x^{\frac{9}{4}} \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)^{2}}\right)}{64 \left(\left(\sqrt[4]{x} + 1\right)^{2} + 1\right)}$$
The graph