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How to use it?
- Derivative of:
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Derivative of 3^x
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Derivative of x^(1/2)
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Derivative of x*atan(x)
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Derivative of -2
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Identical expressions
- arcsin(x)*ln(x^ two -exp^x)
- arc sinus of (x) multiply by ln(x squared minus exponent of to the power of x)
- arc sinus of (x) multiply by ln(x to the power of two minus exponent of to the power of x)
- arcsin(x)*ln(x2-expx)
- arcsinx*lnx2-expx
- arcsin(x)*ln(x²-exp^x)
- arcsin(x)*ln(x to the power of 2-exp to the power of x)
- arcsin(x)ln(x^2-exp^x)
- arcsin(x)ln(x2-expx)
- arcsinxlnx2-expx
- arcsinxlnx^2-exp^x
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Similar expressions
- arcsin(x)*ln(x^2+exp^x)
- arcsinx*ln(x^2-exp^x)
Derivative of arcsin(x)*ln(x^2-exp^x)
The solution
You have entered
[src]
/ 2 x\ asin(x)*log\x - e /
$$\log{\left(x^{2} - e^{x} \right)} \operatorname{asin}{\left(x \right)}$$
d / / 2 x\\ --\asin(x)*log\x - e // dx
$$\frac{d}{d x} \log{\left(x^{2} - e^{x} \right)} \operatorname{asin}{\left(x \right)}$$
The first derivative
[src]
/ 2 x\ / x \ log\x - e / \- e + 2*x/*asin(x) ------------ + -------------------- ________ 2 x / 2 x - e \/ 1 - x
$$\frac{\left(2 x - e^{x}\right) \operatorname{asin}{\left(x \right)}}{x^{2} - e^{x}} + \frac{\log{\left(x^{2} - e^{x} \right)}}{\sqrt{1 - x^{2}}}$$
The second derivative
[src]
/ 2 \
| / x \ |
| \- e + 2*x/ x|
|-2 + ------------- + e |*asin(x)
/ 2 x\ | 2 x | / x \
x*log\x - e / \ x - e / 2*\- e + 2*x/
-------------- - --------------------------------- + ---------------------
3/2 2 x ________
/ 2\ x - e / 2 / 2 x\
\1 - x / \/ 1 - x *\x - e /
$$\frac{x \log{\left(x^{2} - e^{x} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\left(\frac{\left(2 x - e^{x}\right)^{2}}{x^{2} - e^{x}} + e^{x} - 2\right) \operatorname{asin}{\left(x \right)}}{x^{2} - e^{x}} + \frac{2 \cdot \left(2 x - e^{x}\right)}{\sqrt{1 - x^{2}} \left(x^{2} - e^{x}\right)}$$
The third derivative
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/ 3 \
| / x \ / x\ / x \| / 2 \
| x 2*\- e + 2*x/ 3*\-2 + e /*\- e + 2*x/| / 2 \ | / x \ |
|- e + --------------- + ------------------------|*asin(x) | 3*x | / 2 x\ | \- e + 2*x/ x|
| 2 2 x | |-1 + -------|*log\x - e / 3*|-2 + ------------- + e |
| / 2 x\ x - e | | 2| | 2 x | / x \
\ \x - e / / \ -1 + x / \ x - e / 3*x*\- e + 2*x/
----------------------------------------------------------- - --------------------------- - --------------------------- + ---------------------
2 x 3/2 ________ 3/2
x - e / 2\ / 2 / 2 x\ / 2\ / 2 x\
\1 - x / \/ 1 - x *\x - e / \1 - x / *\x - e /
$$\frac{3 x \left(2 x - e^{x}\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{2} - e^{x}\right)} + \frac{\left(\frac{2 \left(2 x - e^{x}\right)^{3}}{\left(x^{2} - e^{x}\right)^{2}} + \frac{3 \cdot \left(2 x - e^{x}\right) \left(e^{x} - 2\right)}{x^{2} - e^{x}} - e^{x}\right) \operatorname{asin}{\left(x \right)}}{x^{2} - e^{x}} - \frac{3 \left(\frac{\left(2 x - e^{x}\right)^{2}}{x^{2} - e^{x}} + e^{x} - 2\right)}{\sqrt{1 - x^{2}} \left(x^{2} - e^{x}\right)} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \log{\left(x^{2} - e^{x} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$
The graph