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 2x^2-x
-
Derivative of 1/(2x)
-
Derivative of y=3x²+5x+4
-
Derivative of x*sin(2*x)
-
Identical expressions
- (arcsin(3x))^ four
- (arc sinus of (3x)) to the power of 4
- (arc sinus of (3x)) to the power of four
- (arcsin(3x))4
- arcsin3x4
- (arcsin(3x))⁴
- arcsin3x^4
Derivative of (arcsin(3x))^4
The solution
You have entered
[src]
4 asin (3*x)
$$\operatorname{asin}^{4}{\left(3 x \right)}$$
d / 4 \ --\asin (3*x)/ dx
$$\frac{d}{d x} \operatorname{asin}^{4}{\left(3 x \right)}$$
The first derivative
[src]
3 12*asin (3*x) ------------- __________ / 2 \/ 1 - 9*x
$$\frac{12 \operatorname{asin}^{3}{\left(3 x \right)}}{\sqrt{- 9 x^{2} + 1}}$$
The second derivative
[src]
2 / 1 x*asin(3*x) \
108*asin (3*x)*|- --------- + -------------|
| 2 3/2|
| -1 + 9*x / 2\ |
\ \1 - 9*x / /
$$108 \left(\frac{x \operatorname{asin}{\left(3 x \right)}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{9 x^{2} - 1}\right) \operatorname{asin}^{2}{\left(3 x \right)}$$
The third derivative
[src]
/ 2 2 2 \
| 6 asin (3*x) 27*x*asin(3*x) 27*x *asin (3*x)|
108*|------------- + ------------- + -------------- + ----------------|*asin(3*x)
| 3/2 3/2 2 5/2 |
|/ 2\ / 2\ / 2\ / 2\ |
\\1 - 9*x / \1 - 9*x / \-1 + 9*x / \1 - 9*x / /
$$108 \cdot \left(\frac{27 x \operatorname{asin}{\left(3 x \right)}}{\left(9 x^{2} - 1\right)^{2}} + \frac{27 x^{2} \operatorname{asin}^{2}{\left(3 x \right)}}{\left(- 9 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{\operatorname{asin}^{2}{\left(3 x \right)}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}{\left(3 x \right)}$$
The graph