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- Derivative of:
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Derivative of sin(x)^2
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Derivative of y=cos9x
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Derivative of x^3-5x^2+x
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Derivative of log((x+1)/(x-1))
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Identical expressions
- arccos(sin(x))^ three
- arc co sinus of e of ( sinus of (x)) cubed
- arc co sinus of e of ( sinus of (x)) to the power of three
- arccos(sin(x))3
- arccossinx3
- arccos(sin(x))³
- arccos(sin(x)) to the power of 3
- arccossinx^3
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Similar expressions
- arccos(sinx)^3
Derivative of arccos(sin(x))^3
The solution
You have entered
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3 acos (sin(x))
$$\operatorname{acos}^{3}{\left(\sin{\left(x \right)} \right)}$$
acos(sin(x))^3
The first derivative
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2
-3*acos (sin(x))*cos(x)
-----------------------
_____________
/ 2
\/ 1 - sin (x)
$$- \frac{3 \cos{\left(x \right)} \operatorname{acos}^{2}{\left(\sin{\left(x \right)} \right)}}{\sqrt{1 - \sin^{2}{\left(x \right)}}}$$
The second derivative
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/ 2 2 \ | 2*cos (x) acos(sin(x))*sin(x) cos (x)*acos(sin(x))*sin(x)| 3*|- ------------ + ------------------- - ---------------------------|*acos(sin(x)) | 2 _____________ 3/2 | | -1 + sin (x) / 2 / 2 \ | \ \/ 1 - sin (x) \1 - sin (x)/ /
$$3 \left(- \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} - 1} + \frac{\sin{\left(x \right)} \operatorname{acos}{\left(\sin{\left(x \right)} \right)}}{\sqrt{1 - \sin^{2}{\left(x \right)}}} - \frac{\sin{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{acos}{\left(\sin{\left(x \right)} \right)}}{\left(1 - \sin^{2}{\left(x \right)}\right)^{\frac{3}{2}}}\right) \operatorname{acos}{\left(\sin{\left(x \right)} \right)}$$
The third derivative
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/ 2 2 2 2 2 2 2 2 2 2 \ | acos (sin(x)) 2*cos (x) acos (sin(x))*cos (x) 3*acos (sin(x))*sin (x) 6*acos(sin(x))*sin(x) 3*acos (sin(x))*cos (x)*sin (x) 6*cos (x)*acos(sin(x))*sin(x)| 3*|---------------- - ---------------- - --------------------- + ----------------------- + --------------------- - ------------------------------- + -----------------------------|*cos(x) | _____________ 3/2 3/2 3/2 2 5/2 2 | | / 2 / 2 \ / 2 \ / 2 \ -1 + sin (x) / 2 \ / 2 \ | \\/ 1 - sin (x) \1 - sin (x)/ \1 - sin (x)/ \1 - sin (x)/ \1 - sin (x)/ \-1 + sin (x)/ /
$$3 \left(\frac{6 \sin{\left(x \right)} \operatorname{acos}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} - 1} + \frac{6 \sin{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{acos}{\left(\sin{\left(x \right)} \right)}}{\left(\sin^{2}{\left(x \right)} - 1\right)^{2}} + \frac{\operatorname{acos}^{2}{\left(\sin{\left(x \right)} \right)}}{\sqrt{1 - \sin^{2}{\left(x \right)}}} + \frac{3 \sin^{2}{\left(x \right)} \operatorname{acos}^{2}{\left(\sin{\left(x \right)} \right)}}{\left(1 - \sin^{2}{\left(x \right)}\right)^{\frac{3}{2}}} - \frac{\cos^{2}{\left(x \right)} \operatorname{acos}^{2}{\left(\sin{\left(x \right)} \right)}}{\left(1 - \sin^{2}{\left(x \right)}\right)^{\frac{3}{2}}} - \frac{2 \cos^{2}{\left(x \right)}}{\left(1 - \sin^{2}{\left(x \right)}\right)^{\frac{3}{2}}} - \frac{3 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{acos}^{2}{\left(\sin{\left(x \right)} \right)}}{\left(1 - \sin^{2}{\left(x \right)}\right)^{\frac{5}{2}}}\right) \cos{\left(x \right)}$$