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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of ((x-1)/(x+1))^4
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Derivative of (x-1)/(2*x+3)
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Derivative of sin(x)/(x+1)
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Derivative of sin(x)+(3*x)^6
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Identical expressions
- arcsin^ two *(5x)
- arc sinus of squared multiply by (5x)
- arc sinus of to the power of two multiply by (5x)
- arcsin2*(5x)
- arcsin2*5x
- arcsin²*(5x)
- arcsin to the power of 2*(5x)
- arcsin^2(5x)
- arcsin2(5x)
- arcsin25x
- arcsin^25x
Derivative of arcsin^2*(5x)
The solution
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2 asin (5*x)
$$\operatorname{asin}^{2}{\left(5 x \right)}$$
d / 2 \ --\asin (5*x)/ dx
$$\frac{d}{d x} \operatorname{asin}^{2}{\left(5 x \right)}$$
The first derivative
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10*asin(5*x) -------------- ___________ / 2 \/ 1 - 25*x
$$\frac{10 \operatorname{asin}{\left(5 x \right)}}{\sqrt{- 25 x^{2} + 1}}$$
The second derivative
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/ 1 5*x*asin(5*x) \ 50*|- ---------- + --------------| | 2 3/2| | -1 + 25*x / 2\ | \ \1 - 25*x / /
$$50 \cdot \left(\frac{5 x \operatorname{asin}{\left(5 x \right)}}{\left(- 25 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{25 x^{2} - 1}\right)$$
The third derivative
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/ 2 \
| asin(5*x) 15*x 75*x *asin(5*x)|
250*|-------------- + ------------- + ---------------|
| 3/2 2 5/2|
|/ 2\ / 2\ / 2\ |
\\1 - 25*x / \-1 + 25*x / \1 - 25*x / /
$$250 \cdot \left(\frac{15 x}{\left(25 x^{2} - 1\right)^{2}} + \frac{75 x^{2} \operatorname{asin}{\left(5 x \right)}}{\left(- 25 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{\operatorname{asin}{\left(5 x \right)}}{\left(- 25 x^{2} + 1\right)^{\frac{3}{2}}}\right)$$
The graph