Mister Exam
Other calculators
- 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 f(x)=2x-3
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Derivative of y=x(x-1)
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Derivative of (x+3)^2*e^(2-x)
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Derivative of (x^2+8)/(x-1)
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Identical expressions
- (asint×acost)
- ( arc sinus of e of t× arc co sinus of e of ine of t)
- asint×acost
Derivative of (asint×acost)
The solution
You have entered
[src]
asin(t)*acos(t)
$$\operatorname{acos}{\left(t \right)} \operatorname{asin}{\left(t \right)}$$
asin(t)*acos(t)
The first derivative
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acos(t) asin(t) ----------- - ----------- ________ ________ / 2 / 2 \/ 1 - t \/ 1 - t
$$\frac{\operatorname{acos}{\left(t \right)}}{\sqrt{1 - t^{2}}} - \frac{\operatorname{asin}{\left(t \right)}}{\sqrt{1 - t^{2}}}$$
The second derivative
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2 t*acos(t) t*asin(t)
------- + ----------- - -----------
2 3/2 3/2
-1 + t / 2\ / 2\
\1 - t / \1 - t /
$$\frac{t \operatorname{acos}{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}}} - \frac{t \operatorname{asin}{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}}} + \frac{2}{t^{2} - 1}$$
The third derivative
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/ 2 \ / 2 \
| 3*t | | 3*t |
|-1 + -------|*asin(t) |-1 + -------|*acos(t)
| 2| | 2|
6*t \ -1 + t / \ -1 + t /
- ---------- + ---------------------- - ----------------------
2 3/2 3/2
/ 2\ / 2\ / 2\
\-1 + t / \1 - t / \1 - t /
$$- \frac{6 t}{\left(t^{2} - 1\right)^{2}} - \frac{\left(\frac{3 t^{2}}{t^{2} - 1} - 1\right) \operatorname{acos}{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{3 t^{2}}{t^{2} - 1} - 1\right) \operatorname{asin}{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}}}$$