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How to use it?
- Derivative of:
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Derivative of 3*x^2
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Derivative of -1/x
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Derivative of x^(1/3)
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Derivative of x^3*e^x
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Identical expressions
- y=tgx/ three -ctg2x+arcsin5x
- y equally tgx divide by 3 minus ctg2x plus arc sinus of 5x
- y equally tgx divide by three minus ctg2x plus arc sinus of 5x
- y=tgx divide by 3-ctg2x+arcsin5x
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Similar expressions
- y=tgx/3-ctg2x-arcsin5x
- y=tgx/3+ctg2x+arcsin5x
Derivative of y=tgx/3-ctg2x+arcsin5x
The solution
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[src]
tan(x) ------ - cot(2*x) + asin(5*x) 3
$$\left(\frac{\tan{\left(x \right)}}{3} - \cot{\left(2 x \right)}\right) + \operatorname{asin}{\left(5 x \right)}$$
tan(x)/3 - cot(2*x) + asin(5*x)
The first derivative
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2
7 2 5 tan (x)
- + 2*cot (2*x) + -------------- + -------
3 ___________ 3
/ 2
\/ 1 - 25*x
$$\frac{\tan^{2}{\left(x \right)}}{3} + 2 \cot^{2}{\left(2 x \right)} + \frac{7}{3} + \frac{5}{\sqrt{1 - 25 x^{2}}}$$
The second derivative
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/ 2 \
/ 2 \ 125*x 2*\1 + tan (x)/*tan(x)
- 8*\1 + cot (2*x)/*cot(2*x) + -------------- + ----------------------
3/2 3
/ 2\
\1 - 25*x /
$$\frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{3} - 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)}$$
The third derivative
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2
2 / 2 \ 2 2 / 2 \
/ 2 \ 125 2*\1 + tan (x)/ 2 / 2 \ 9375*x 4*tan (x)*\1 + tan (x)/
16*\1 + cot (2*x)/ + -------------- + ---------------- + 32*cot (2*x)*\1 + cot (2*x)/ + -------------- + -----------------------
3/2 3 5/2 3
/ 2\ / 2\
\1 - 25*x / \1 - 25*x /
$$\frac{9375 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{3} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{3} + 16 \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} + 32 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot^{2}{\left(2 x \right)} + \frac{125}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}$$
The graph