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 x^2+cos(x)
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Derivative of (x+1)^2*(x-5)-6
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Derivative of log(11*x)
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Derivative of e^x-2
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Identical expressions
- (asint)/(cost)^ two
- ( arc sinus of e of t) divide by ( co sinus of e of t) squared
- ( arc sinus of e of t) divide by ( co sinus of e of t) to the power of two
- (asint)/(cost)2
- asint/cost2
- (asint)/(cost)²
- (asint)/(cost) to the power of 2
- asint/cost^2
- (asint) divide by (cost)^2
Derivative of (asint)/(cost)^2
The solution
You have entered
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asin(t) ------- 2 cos (t)
$$\frac{\operatorname{asin}{\left(t \right)}}{\cos^{2}{\left(t \right)}}$$
asin(t)/cos(t)^2
The first derivative
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1 2*asin(t)*sin(t) ------------------- + ---------------- ________ 3 / 2 2 cos (t) \/ 1 - t *cos (t)
$$\frac{2 \sin{\left(t \right)} \operatorname{asin}{\left(t \right)}}{\cos^{3}{\left(t \right)}} + \frac{1}{\sqrt{1 - t^{2}} \cos^{2}{\left(t \right)}}$$
The second derivative
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/ 2 \
t | 3*sin (t)| 4*sin(t)
----------- + 2*|1 + ---------|*asin(t) + ------------------
3/2 | 2 | ________
/ 2\ \ cos (t) / / 2
\1 - t / \/ 1 - t *cos(t)
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2
cos (t)
$$\frac{\frac{t}{\left(1 - t^{2}\right)^{\frac{3}{2}}} + 2 \left(\frac{3 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \operatorname{asin}{\left(t \right)} + \frac{4 \sin{\left(t \right)}}{\sqrt{1 - t^{2}} \cos{\left(t \right)}}}{\cos^{2}{\left(t \right)}}$$
The third derivative
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2 / 2 \ / 2 \
3*t | 3*sin (t)| | 3*sin (t)|
-1 + ------- 6*|1 + ---------| 8*|2 + ---------|*asin(t)*sin(t)
2 | 2 | | 2 |
-1 + t \ cos (t) / 6*t*sin(t) \ cos (t) /
- ------------ + ----------------- + ------------------ + --------------------------------
3/2 ________ 3/2 cos(t)
/ 2\ / 2 / 2\
\1 - t / \/ 1 - t \1 - t / *cos(t)
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2
cos (t)
$$\frac{\frac{6 t \sin{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}} \cos{\left(t \right)}} + \frac{8 \left(\frac{3 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 2\right) \sin{\left(t \right)} \operatorname{asin}{\left(t \right)}}{\cos{\left(t \right)}} + \frac{6 \left(\frac{3 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)}{\sqrt{1 - t^{2}}} - \frac{\frac{3 t^{2}}{t^{2} - 1} - 1}{\left(1 - t^{2}\right)^{\frac{3}{2}}}}{\cos^{2}{\left(t \right)}}$$