Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of e^x/x^2
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Derivative of cos(x)/x^2
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Derivative of cos(sqrt(x))
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Derivative of cos(1/x)
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Identical expressions
- arccos(sqrt(tan(x)))
- arc co sinus of e of ( square root of ( tangent of (x)))
- arccos(√(tan(x)))
- arccossqrttanx
Derivative of arccos(sqrt(tan(x)))
The solution
You have entered
[src]
/ ________\ acos\\/ tan(x) /
$$\operatorname{acos}{\left(\sqrt{\tan{\left(x \right)}} \right)}$$
acos(sqrt(tan(x)))
The first derivative
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/ 2 \
|1 tan (x)|
-|- + -------|
\2 2 /
-------------------------
____________ ________
\/ 1 - tan(x) *\/ tan(x)
$$- \frac{\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}}{\sqrt{1 - \tan{\left(x \right)}} \sqrt{\tan{\left(x \right)}}}$$
The second derivative
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/ 2 2 \
/ 2 \ | ________ 1 + tan (x) 1 + tan (x) |
\1 + tan (x)/*|- \/ tan(x) + ----------- - -------------------------|
| 3/2 ________|
\ 4*tan (x) 4*(1 - tan(x))*\/ tan(x) /
----------------------------------------------------------------------
____________
\/ 1 - tan(x)
$$\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{4 \tan^{\frac{3}{2}}{\left(x \right)}} - \sqrt{\tan{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{4 \left(1 - \tan{\left(x \right)}\right) \sqrt{\tan{\left(x \right)}}}\right)}{\sqrt{1 - \tan{\left(x \right)}}}$$
The third derivative
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/ 2 2 2 \
| 2 / 2 \ ________ / 2 \ / 2 \ / 2 \ |
/ 2 \ | 3/2 1 + tan (x) 3*\1 + tan (x)/ 3*\/ tan(x) *\1 + tan (x)/ 3*\1 + tan (x)/ \1 + tan (x)/ |
\1 + tan (x)/*|- 2*tan (x) + ------------ - ---------------- - -------------------------- - -------------------------- + ------------------------|
| ________ 5/2 2*(1 - tan(x)) 2 ________ 3/2 |
\ 2*\/ tan(x) 8*tan (x) 8*(1 - tan(x)) *\/ tan(x) 4*(1 - tan(x))*tan (x)/
----------------------------------------------------------------------------------------------------------------------------------------------------
____________
\/ 1 - tan(x)
$$\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{8 \tan^{\frac{5}{2}}{\left(x \right)}} + \frac{\tan^{2}{\left(x \right)} + 1}{2 \sqrt{\tan{\left(x \right)}}} - 2 \tan^{\frac{3}{2}}{\left(x \right)} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{4 \left(1 - \tan{\left(x \right)}\right) \tan^{\frac{3}{2}}{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\tan{\left(x \right)}}}{2 \left(1 - \tan{\left(x \right)}\right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{8 \left(1 - \tan{\left(x \right)}\right)^{2} \sqrt{\tan{\left(x \right)}}}\right)}{\sqrt{1 - \tan{\left(x \right)}}}$$