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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 1/2*x^2
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Derivative of -(x^2+1)/x
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Derivative of sin(x)-cos(x)
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Derivative of e^(1/x)
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Identical expressions
- y=tg(x/ three)-ctg2x+arcsin5x
- y equally tg(x divide by 3) minus ctg2x plus arc sinus of 5x
- y equally tg(x divide by three) minus ctg2x plus arc sinus of 5x
- y=tgx/3-ctg2x+arcsin5x
- y=tg(x divide by 3)-ctg2x+arcsin5x
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Similar expressions
- y=tgx/3-ctg2x+arcsin5x
- y=tg(x/3)-ctg2x-arcsin5x
- y=tg(x/3)+ctg2x+arcsin5x
Derivative of y=tg(x/3)-ctg2x+arcsin5x
The solution
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[src]
/x\ tan|-| - cot(2*x) + asin(5*x) \3/
$$\left(\tan{\left(\frac{x}{3} \right)} - \cot{\left(2 x \right)}\right) + \operatorname{asin}{\left(5 x \right)}$$
tan(x/3) - cot(2*x) + asin(5*x)
The first derivative
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2/x\
tan |-|
7 2 5 \3/
- + 2*cot (2*x) + -------------- + -------
3 ___________ 3
/ 2
\/ 1 - 25*x
$$\frac{\tan^{2}{\left(\frac{x}{3} \right)}}{3} + 2 \cot^{2}{\left(2 x \right)} + \frac{7}{3} + \frac{5}{\sqrt{1 - 25 x^{2}}}$$
The second derivative
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/ 2/x\\ /x\
2*|1 + tan |-||*tan|-|
/ 2 \ 125*x \ \3// \3/
- 8*\1 + cot (2*x)/*cot(2*x) + -------------- + ----------------------
3/2 9
/ 2\
\1 - 25*x /
$$\frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{2 \left(\tan^{2}{\left(\frac{x}{3} \right)} + 1\right) \tan{\left(\frac{x}{3} \right)}}{9} - 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)}$$
The third derivative
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2
/ 2/x\\ 2/x\ / 2/x\\
2 2*|1 + tan |-|| 2 4*tan |-|*|1 + tan |-||
/ 2 \ 125 \ \3// 2 / 2 \ 9375*x \3/ \ \3//
16*\1 + cot (2*x)/ + -------------- + ---------------- + 32*cot (2*x)*\1 + cot (2*x)/ + -------------- + -----------------------
3/2 27 5/2 27
/ 2\ / 2\
\1 - 25*x / \1 - 25*x /
$$\frac{9375 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{2 \left(\tan^{2}{\left(\frac{x}{3} \right)} + 1\right)^{2}}{27} + \frac{4 \left(\tan^{2}{\left(\frac{x}{3} \right)} + 1\right) \tan^{2}{\left(\frac{x}{3} \right)}}{27} + 16 \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} + 32 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot^{2}{\left(2 x \right)} + \frac{125}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}$$
The graph