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 (1+tan(3*x)^(2))*e^(-x/2)
-
Derivative of 13*x-13*tan(x)-18
-
Derivative of (0,5-x)cosx+sinx
-
Derivative of -x/(x^2+289)
-
Identical expressions
- lg(x+ two)*(arcsin(3x))^ two
- lg(x plus 2) multiply by (arc sinus of (3x)) squared
- lg(x plus two) multiply by (arc sinus of (3x)) to the power of two
- lg(x+2)*(arcsin(3x))2
- lgx+2*arcsin3x2
- lg(x+2)*(arcsin(3x))²
- lg(x+2)*(arcsin(3x)) to the power of 2
- lg(x+2)(arcsin(3x))^2
- lg(x+2)(arcsin(3x))2
- lgx+2arcsin3x2
- lgx+2arcsin3x^2
-
Similar expressions
- lg(x-2)*(arcsin(3x))^2
Derivative of lg(x+2)*(arcsin(3x))^2
The solution
You have entered
[src]
2 log(x + 2)*asin (3*x)
$$\log{\left(x + 2 \right)} \operatorname{asin}^{2}{\left(3 x \right)}$$
d / 2 \ --\log(x + 2)*asin (3*x)/ dx
$$\frac{d}{d x} \log{\left(x + 2 \right)} \operatorname{asin}^{2}{\left(3 x \right)}$$
The first derivative
[src]
2
asin (3*x) 6*asin(3*x)*log(x + 2)
---------- + ----------------------
x + 2 __________
/ 2
\/ 1 - 9*x
$$\frac{\operatorname{asin}^{2}{\left(3 x \right)}}{x + 2} + \frac{6 \log{\left(x + 2 \right)} \operatorname{asin}{\left(3 x \right)}}{\sqrt{- 9 x^{2} + 1}}$$
The second derivative
[src]
2
asin (3*x) / 1 3*x*asin(3*x)\ 12*asin(3*x)
- ---------- + 18*|- --------- + -------------|*log(2 + x) + ---------------------
2 | 2 3/2| __________
(2 + x) | -1 + 9*x / 2\ | / 2
\ \1 - 9*x / / \/ 1 - 9*x *(2 + x)
$$18 \cdot \left(\frac{3 x \operatorname{asin}{\left(3 x \right)}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{9 x^{2} - 1}\right) \log{\left(x + 2 \right)} - \frac{\operatorname{asin}^{2}{\left(3 x \right)}}{\left(x + 2\right)^{2}} + \frac{12 \operatorname{asin}{\left(3 x \right)}}{\sqrt{- 9 x^{2} + 1} \left(x + 2\right)}$$
The third derivative
[src]
/ / 1 3*x*asin(3*x)\ \ | 27*|- --------- + -------------| | | | 2 3/2| | | 2 | -1 + 9*x / 2\ | / 2 \ | |asin (3*x) \ \1 - 9*x / / | asin(3*x) 9*x 27*x *asin(3*x)| 9*asin(3*x) | 2*|---------- + -------------------------------- + 27*|------------- + ------------ + ---------------|*log(2 + x) - ----------------------| | 3 2 + x | 3/2 2 5/2 | __________ | | (2 + x) |/ 2\ / 2\ / 2\ | / 2 2| \ \\1 - 9*x / \-1 + 9*x / \1 - 9*x / / \/ 1 - 9*x *(2 + x) /
$$2 \cdot \left(27 \cdot \left(\frac{9 x}{\left(9 x^{2} - 1\right)^{2}} + \frac{27 x^{2} \operatorname{asin}{\left(3 x \right)}}{\left(- 9 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{\operatorname{asin}{\left(3 x \right)}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left(x + 2 \right)} + \frac{27 \cdot \left(\frac{3 x \operatorname{asin}{\left(3 x \right)}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{9 x^{2} - 1}\right)}{x + 2} + \frac{\operatorname{asin}^{2}{\left(3 x \right)}}{\left(x + 2\right)^{3}} - \frac{9 \operatorname{asin}{\left(3 x \right)}}{\sqrt{- 9 x^{2} + 1} \left(x + 2\right)^{2}}\right)$$
The graph