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^5+1)
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Derivative of x^sqrt(x)
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Derivative of log(x+2)
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Derivative of ex^2
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Identical expressions
- (arcsin(x^ two))/ln(3x)
- (arc sinus of (x squared )) divide by ln(3x)
- (arc sinus of (x to the power of two)) divide by ln(3x)
- (arcsin(x2))/ln(3x)
- arcsinx2/ln3x
- (arcsin(x²))/ln(3x)
- (arcsin(x to the power of 2))/ln(3x)
- arcsinx^2/ln3x
- (arcsin(x^2)) divide by ln(3x)
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What you mean?
- asin(x^2)/log(3*x)
- asin(x^2)/((log(3)*x))
- asin(x^2)*3*x/log(x)
- asin(x^2)/log(3*x)
- asin(x^2)/((log(3)*x))
- asin(x^2)*3*x/log(x)
- asin(x^2)*3*x/log(x)
You entered:
(arcsin(x^2))/ln(3x)
What you mean?
Derivative of (arcsin(x^2))/ln(3x)
The solution
You have entered
[src]
/ 2\ asin\x / -------- log(3*x)
$$\frac{\operatorname{asin}{\left(x^{2} \right)}}{\log{\left(3 x \right)}}$$
/ / 2\\ d |asin\x /| --|--------| dx\log(3*x)/
$$\frac{d}{d x} \frac{\operatorname{asin}{\left(x^{2} \right)}}{\log{\left(3 x \right)}}$$
The first derivative
[src]
/ 2\
asin\x / 2*x
- ----------- + --------------------
2 ________
x*log (3*x) / 4
\/ 1 - x *log(3*x)
$$\frac{2 x}{\sqrt{1 - x^{4}} \log{\left(3 x \right)}} - \frac{\operatorname{asin}{\left(x^{2} \right)}}{x \log{\left(3 x \right)}^{2}}$$
The second derivative
[src]
/ 4 \
| 2*x |
2*|-1 + -------| / 2 \ / 2\
| 4| |1 + --------|*asin\x /
4 \ -1 + x / \ log(3*x)/
- -------------------- - ---------------- + -----------------------
________ ________ 2
/ 4 / 4 x *log(3*x)
\/ 1 - x *log(3*x) \/ 1 - x
-------------------------------------------------------------------
log(3*x)
$$\frac{- \frac{2 \cdot \left(\frac{2 x^{4}}{x^{4} - 1} - 1\right)}{\sqrt{1 - x^{4}}} - \frac{4}{\sqrt{1 - x^{4}} \log{\left(3 x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(3 x \right)}}\right) \operatorname{asin}{\left(x^{2} \right)}}{x^{2} \log{\left(3 x \right)}}}{\log{\left(3 x \right)}}$$
The third derivative
[src]
/ / 4 \ / 4 \ \
| 3 | 6*x | / 3 3 \ / 2\ | 2*x | |
| 2*x *|-5 + -------| |1 + -------- + ---------|*asin\x / / 2 \ 3*|-1 + -------| |
| | 4| | log(3*x) 2 | 3*|1 + --------| | 4| |
| \ -1 + x / \ log (3*x)/ \ log(3*x)/ \ -1 + x / |
2*|- ------------------- - ----------------------------------- + ---------------------- + ----------------------|
| 3/2 3 ________ ________ |
| / 4\ x *log(3*x) / 4 / 4 |
\ \1 - x / x*\/ 1 - x *log(3*x) x*\/ 1 - x *log(3*x)/
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log(3*x)
$$\frac{2 \left(- \frac{2 x^{3} \cdot \left(\frac{6 x^{4}}{x^{4} - 1} - 5\right)}{\left(1 - x^{4}\right)^{\frac{3}{2}}} + \frac{3 \cdot \left(1 + \frac{2}{\log{\left(3 x \right)}}\right)}{x \sqrt{1 - x^{4}} \log{\left(3 x \right)}} + \frac{3 \cdot \left(\frac{2 x^{4}}{x^{4} - 1} - 1\right)}{x \sqrt{1 - x^{4}} \log{\left(3 x \right)}} - \frac{\left(1 + \frac{3}{\log{\left(3 x \right)}} + \frac{3}{\log{\left(3 x \right)}^{2}}\right) \operatorname{asin}{\left(x^{2} \right)}}{x^{3} \log{\left(3 x \right)}}\right)}{\log{\left(3 x \right)}}$$
The graph