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
-
How to use it?
- Derivative of:
-
Derivative of e^(2*cos(t)^(2)-2*sin(t)^(2))
-
Derivative of 5x^3
-
Derivative of 4*sqrt(x)
-
Derivative of 3*sqrt(x)
-
Identical expressions
- arccos*sqrt(x)
- arc co sinus of e of multiply by square root of (x)
- arccos*√(x)
- arccossqrt(x)
- arccossqrtx
-
Similar expressions
- arccossqrt(x)*sinx^2*e^cos2x
- y=(x+1)^(arccossqrt(x))
- -sqrt(3)/(6*x*sqrt(1-x))-(sqrt(3)*arccos(sqrt(x)))/(6*x*sqrt(x))
- arccos(sqrtx)+sqrt(x-x^2)
- arccos((sqrt(x))/(1+x))
Derivative of arccos*sqrt(x)
The solution
You have entered
[src]
___ acos(x)*\/ x
$$\sqrt{x} \operatorname{acos}{\left(x \right)}$$
acos(x)*sqrt(x)
The first derivative
[src]
___
acos(x) \/ x
------- - -----------
___ ________
2*\/ x / 2
\/ 1 - x
$$- \frac{\sqrt{x}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2 \sqrt{x}}$$
The second derivative
[src]
/ 3/2 \ | 1 x acos(x)| -|----------------- + ----------- + -------| | ________ 3/2 3/2| | ___ / 2 / 2\ 4*x | \\/ x *\/ 1 - x \1 - x / /
$$- (\frac{x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{4 x^{\frac{3}{2}}})$$
The third derivative
[src]
/ 2 \
___ | 3*x |
\/ x *|-1 + -------|
___ | 2|
3*\/ x 3 3*acos(x) \ -1 + x /
- ------------- + ------------------ + --------- + --------------------
3/2 ________ 5/2 3/2
/ 2\ 3/2 / 2 8*x / 2\
2*\1 - x / 4*x *\/ 1 - x \1 - x /
$$\frac{\sqrt{x} \left(\frac{3 x^{2}}{x^{2} - 1} - 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3 \sqrt{x}}{2 \left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{4 x^{\frac{3}{2}} \sqrt{1 - x^{2}}} + \frac{3 \operatorname{acos}{\left(x \right)}}{8 x^{\frac{5}{2}}}$$