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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of e^x^2
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Derivative of tanh(x)
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Derivative of cos²x
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Derivative of (π-2x)³
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Identical expressions
- five arcsinsqrt(2x^ four -5)+ seven
- 5arc sinus of square root of (2x to the power of 4 minus 5) plus 7
- five arc sinus of square root of (2x to the power of four minus 5) plus seven
- 5arcsin√(2x^4-5)+7
- 5arcsinsqrt(2x4-5)+7
- 5arcsinsqrt2x4-5+7
- 5arcsinsqrt(2x⁴-5)+7
- 5arcsinsqrt2x^4-5+7
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Similar expressions
- 5arcsinsqrt(2x^4-5)-7
- 5arcsinsqrt(2x^4+5)+7
Derivative of 5arcsinsqrt(2x^4-5)+7
The solution
You have entered
[src]
/ __________\
| / 4 |
5*asin\\/ 2*x - 5 / + 7
$$5 \operatorname{asin}{\left(\sqrt{2 x^{4} - 5} \right)} + 7$$
5*asin(sqrt(2*x^4 - 5)) + 7
The first derivative
[src]
3
20*x
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__________ __________
/ 4 / 4
\/ 6 - 2*x *\/ 2*x - 5
$$\frac{20 x^{3}}{\sqrt{6 - 2 x^{4}} \sqrt{2 x^{4} - 5}}$$
The second derivative
[src]
/ 4 4 \
___ 2 | 4*x 2*x |
10*\/ 2 *x *|3 - --------- + ------|
| 4 4|
\ -5 + 2*x 3 - x /
------------------------------------
___________ ________
/ 4 / 4
\/ -5 + 2*x *\/ 3 - x
$$\frac{10 \sqrt{2} x^{2} \left(- \frac{4 x^{4}}{2 x^{4} - 5} + \frac{2 x^{4}}{3 - x^{4}} + 3\right)}{\sqrt{3 - x^{4}} \sqrt{2 x^{4} - 5}}$$
The third derivative
[src]
/ 4 8 4 8 8 \
___ | 18*x 6*x 9*x 24*x 8*x |
20*x*\/ 2 *|3 - --------- + --------- + ------ + ------------ - --------------------|
| 4 2 4 2 / 4\ / 4\|
| -5 + 2*x / 4\ 3 - x / 4\ \-5 + 2*x /*\3 - x /|
\ \3 - x / \-5 + 2*x / /
-------------------------------------------------------------------------------------
___________ ________
/ 4 / 4
\/ -5 + 2*x *\/ 3 - x
$$\frac{20 \sqrt{2} x \left(\frac{24 x^{8}}{\left(2 x^{4} - 5\right)^{2}} - \frac{8 x^{8}}{\left(3 - x^{4}\right) \left(2 x^{4} - 5\right)} + \frac{6 x^{8}}{\left(3 - x^{4}\right)^{2}} - \frac{18 x^{4}}{2 x^{4} - 5} + \frac{9 x^{4}}{3 - x^{4}} + 3\right)}{\sqrt{3 - x^{4}} \sqrt{2 x^{4} - 5}}$$