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 x^-(4/5)
-
Derivative of ln(x^2-2x)
-
Derivative of 6/x^4
-
Derivative of 2*x-x^2
-
Identical expressions
- arcsin(one -x^ four)^ three
- arc sinus of (1 minus x to the power of 4) cubed
- arc sinus of (one minus x to the power of four) to the power of three
- arcsin(1-x4)3
- arcsin1-x43
- arcsin(1-x⁴)³
- arcsin(1-x to the power of 4) to the power of 3
- arcsin1-x^4^3
-
Similar expressions
- arcsin(1+x^4)^3
Derivative of arcsin(1-x^4)^3
The solution
The first derivative
[src]
3 2/ 4\
-12*x *asin \1 - x /
--------------------
_______________
/ 2
/ / 4\
\/ 1 - \1 - x /
$$- \frac{12 x^{3} \operatorname{asin}^{2}{\left(1 - x^{4} \right)}}{\sqrt{1 - \left(1 - x^{4}\right)^{2}}}$$
The second derivative
[src]
/ / 4\ 4 4 / 4\ / 4\\
2 | 3*asin\-1 + x / 8*x 4*x *\-1 + x /*asin\-1 + x /| / 4\
12*x *|- ------------------- + --------------- - ----------------------------|*asin\-1 + x /
| _______________ 2 3/2 |
| / 2 / 4\ / 2\ |
| / / 4\ -1 + \-1 + x / | / 4\ | |
\ \/ 1 - \1 - x / \1 - \1 - x / / /
$$12 x^{2} \left(\frac{8 x^{4}}{\left(x^{4} - 1\right)^{2} - 1} - \frac{4 x^{4} \left(x^{4} - 1\right) \operatorname{asin}{\left(x^{4} - 1 \right)}}{\left(1 - \left(1 - x^{4}\right)^{2}\right)^{\frac{3}{2}}} - \frac{3 \operatorname{asin}{\left(x^{4} - 1 \right)}}{\sqrt{1 - \left(1 - x^{4}\right)^{2}}}\right) \operatorname{asin}{\left(x^{4} - 1 \right)}$$
The third derivative
[src]
/ 2 \
| 8 2/ 4\ 8 2/ 4\ 4 / 4\ 8 / 4\ / 4\ 8 / 4\ 2/ 4\ 4 2/ 4\ / 4\|
| 16*x 3*asin \-1 + x / 8*x *asin \-1 + x / 36*x *asin\-1 + x / 48*x *\-1 + x /*asin\-1 + x / 24*x *\-1 + x / *asin \-1 + x / 18*x *asin \-1 + x /*\-1 + x /|
24*x*|- ------------------ - ------------------- - ------------------- + ------------------- - ----------------------------- - ------------------------------- - ------------------------------|
| 3/2 _______________ 3/2 2 2 5/2 3/2 |
| / 2\ / 2 / 2\ / 4\ / 2\ / 2\ / 2\ |
| | / 4\ | / / 4\ | / 4\ | -1 + \-1 + x / | / 4\ | | / 4\ | | / 4\ | |
\ \1 - \1 - x / / \/ 1 - \1 - x / \1 - \1 - x / / \-1 + \-1 + x / / \1 - \1 - x / / \1 - \1 - x / / /
$$24 x \left(- \frac{48 x^{8} \left(x^{4} - 1\right) \operatorname{asin}{\left(x^{4} - 1 \right)}}{\left(\left(x^{4} - 1\right)^{2} - 1\right)^{2}} - \frac{8 x^{8} \operatorname{asin}^{2}{\left(x^{4} - 1 \right)}}{\left(1 - \left(1 - x^{4}\right)^{2}\right)^{\frac{3}{2}}} - \frac{16 x^{8}}{\left(1 - \left(1 - x^{4}\right)^{2}\right)^{\frac{3}{2}}} - \frac{24 x^{8} \left(x^{4} - 1\right)^{2} \operatorname{asin}^{2}{\left(x^{4} - 1 \right)}}{\left(1 - \left(1 - x^{4}\right)^{2}\right)^{\frac{5}{2}}} + \frac{36 x^{4} \operatorname{asin}{\left(x^{4} - 1 \right)}}{\left(x^{4} - 1\right)^{2} - 1} - \frac{18 x^{4} \left(x^{4} - 1\right) \operatorname{asin}^{2}{\left(x^{4} - 1 \right)}}{\left(1 - \left(1 - x^{4}\right)^{2}\right)^{\frac{3}{2}}} - \frac{3 \operatorname{asin}^{2}{\left(x^{4} - 1 \right)}}{\sqrt{1 - \left(1 - x^{4}\right)^{2}}}\right)$$
The graph