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- Derivative of:
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Derivative of sin(x)+cos(x)
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Derivative of cos(x)^2
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Derivative of sin(x^3)
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Derivative of log(x)^2
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Identical expressions
- 3arcctgx+8x¼-(one /x)³
- 3arcctgx plus 8x¼ minus (1 divide by x)³
- 3arcctgx plus 8x¼ minus (one divide by x)³
- 3arcctgx+8x¼-1/x³
- 3arcctgx+8x¼-(1 divide by x)³
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Similar expressions
- 3arcctgx+8x¼+(1/x)³
- 3arcctgx-8x¼-(1/x)³
Derivative of 3arcctgx+8x¼-(1/x)³
The solution
You have entered
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3
/ 1\
3*acot(x) + 8*x*1/4 - |1*-|
\ x/
$$- \left(1 \cdot \frac{1}{x}\right)^{3} + 8 x \frac{1}{4} + 3 \operatorname{acot}{\left(x \right)}$$
/ 3\ d | / 1\ | --|3*acot(x) + 8*x*1/4 - |1*-| | dx\ \ x/ /
$$\frac{d}{d x} \left(- \left(1 \cdot \frac{1}{x}\right)^{3} + 8 x \frac{1}{4} + 3 \operatorname{acot}{\left(x \right)}\right)$$
The first derivative
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3 3
2 - ------ + --
2 4
1 + x x
$$2 - \frac{3}{x^{2} + 1} + \frac{3}{x^{4}}$$
The second derivative
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/ 2 x \ 6*|- -- + ---------| | 5 2| | x / 2\ | \ \1 + x / /
$$6 \left(\frac{x}{\left(x^{2} + 1\right)^{2}} - \frac{2}{x^{5}}\right)$$
The third derivative
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/ 2 \ | 1 10 4*x | 6*|--------- + -- - ---------| | 2 6 3| |/ 2\ x / 2\ | \\1 + x / \1 + x / /
$$6 \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{3}} + \frac{1}{\left(x^{2} + 1\right)^{2}} + \frac{10}{x^{6}}\right)$$
The graph