Mister Exam
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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 5*x
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Derivative of (1-x^2)^(1/2)
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Derivative of x^(3*x)
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Derivative of (x+1)/(x-1)
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Identical expressions
- y=sin^ three *x+arctg*4x
- y equally sinus of cubed multiply by x plus arctg multiply by 4x
- y equally sinus of to the power of three multiply by x plus arctg multiply by 4x
- y=sin3*x+arctg*4x
- y=sin³*x+arctg*4x
- y=sin to the power of 3*x+arctg*4x
- y=sin^3x+arctg4x
- y=sin3x+arctg4x
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Similar expressions
- y=sin^3*x-arctg*4x
Derivative of y=sin^3*x+arctg*4x
The solution
You have entered
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3 sin (x) + atan(4*x)
$$\sin^{3}{\left(x \right)} + \operatorname{atan}{\left(4 x \right)}$$
d / 3 \ --\sin (x) + atan(4*x)/ dx
$$\frac{d}{d x} \left(\sin^{3}{\left(x \right)} + \operatorname{atan}{\left(4 x \right)}\right)$$
The first derivative
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4 2
--------- + 3*sin (x)*cos(x)
2
1 + 16*x
$$3 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{4}{16 x^{2} + 1}$$
The second derivative
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3 128*x 2
- 3*sin (x) - ------------ + 6*cos (x)*sin(x)
2
/ 2\
\1 + 16*x /
$$- \frac{128 x}{\left(16 x^{2} + 1\right)^{2}} - 3 \sin^{3}{\left(x \right)} + 6 \sin{\left(x \right)} \cos^{2}{\left(x \right)}$$
The third derivative
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2
128 3 2 8192*x
- ------------ + 6*cos (x) - 21*sin (x)*cos(x) + ------------
2 3
/ 2\ / 2\
\1 + 16*x / \1 + 16*x /
$$\frac{8192 x^{2}}{\left(16 x^{2} + 1\right)^{3}} - 21 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 6 \cos^{3}{\left(x \right)} - \frac{128}{\left(16 x^{2} + 1\right)^{2}}$$
The graph