Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of 5-7x
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Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of f(x)=5
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Derivative of 3^(1/x)
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Identical expressions
- arcsin(sqrtx)*lnx
- arc sinus of ( square root of x) multiply by lnx
- arcsin(√x)*lnx
- arcsin(sqrtx)lnx
- arcsinsqrtxlnx
Derivative of arcsin(sqrtx)*lnx
The solution
You have entered
[src]
/ ___\ asin\\/ x /*log(x)
$$\log{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}$$
asin(sqrt(x))*log(x)
The first derivative
[src]
/ ___\
asin\\/ x / log(x)
----------- + -----------------
x ___ _______
2*\/ x *\/ 1 - x
$$\frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
The second derivative
[src]
/1 1 \
/ ___\ |- + ------|*log(x)
1 asin\\/ x / \x -1 + x/
-------------- - ----------- - -------------------
3/2 _______ 2 ___ _______
x *\/ 1 - x x 4*\/ x *\/ 1 - x
$$- \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x^{2}} - \frac{\left(\frac{1}{x - 1} + \frac{1}{x}\right) \log{\left(x \right)}}{4 \sqrt{x} \sqrt{1 - x}} + \frac{1}{x^{\frac{3}{2}} \sqrt{1 - x}}$$
The third derivative
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/3 3 2 \
/1 1 \ |-- + --------- + ----------|*log(x)
/ ___\ 3*|- + ------| | 2 2 x*(-1 + x)|
2*asin\\/ x / 3 \x -1 + x/ \x (-1 + x) /
------------- - ---------------- - ---------------- + ------------------------------------
3 5/2 _______ 3/2 _______ ___ _______
x 2*x *\/ 1 - x 4*x *\/ 1 - x 8*\/ x *\/ 1 - x
$$\frac{2 \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{3}} + \frac{\left(\frac{3}{\left(x - 1\right)^{2}} + \frac{2}{x \left(x - 1\right)} + \frac{3}{x^{2}}\right) \log{\left(x \right)}}{8 \sqrt{x} \sqrt{1 - x}} - \frac{3 \left(\frac{1}{x - 1} + \frac{1}{x}\right)}{4 x^{\frac{3}{2}} \sqrt{1 - x}} - \frac{3}{2 x^{\frac{5}{2}} \sqrt{1 - x}}$$