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How to use it?
- Derivative of:
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Derivative of sin(x)^2
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Derivative of cos(x/3)
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Derivative of √x
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Derivative of 5x-1
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Identical expressions
- one 0x*arccos(sqrt(1-5x))-((log2(x*e))/(cos(2x)))
- 10x multiply by arc co sinus of e of ( square root of (1 minus 5x)) minus (( logarithm of 2(x multiply by e)) divide by ( co sinus of e of (2x)))
- one 0x multiply by arc co sinus of e of ( square root of (1 minus 5x)) minus (( logarithm of 2(x multiply by e)) divide by ( co sinus of e of (2x)))
- 10x*arccos(√(1-5x))-((log2(x*e))/(cos(2x)))
- 10xarccos(sqrt(1-5x))-((log2(xe))/(cos(2x)))
- 10xarccossqrt1-5x-log2xe/cos2x
- 10x*arccos(sqrt(1-5x))-((log2(x*e)) divide by (cos(2x)))
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Similar expressions
- 10x*arccos(sqrt(1+5x))-((log2(x*e))/(cos(2x)))
- 10x*arccos(sqrt(1-5x))+((log2(x*e))/(cos(2x)))
Derivative of 10x*arccos(sqrt(1-5x))-((log2(x*e))/(cos(2x)))
The solution
You have entered
[src]
/log(x*E)\
|--------|
/ _________\ \ log(2) /
10*x*acos\\/ 1 - 5*x / - ----------
cos(2*x)
$$10 x \operatorname{acos}{\left(\sqrt{1 - 5 x} \right)} - \frac{\frac{1}{\log{\left(2 \right)}} \log{\left(e x \right)}}{\cos{\left(2 x \right)}}$$
(10*x)*acos(sqrt(1 - 5*x)) - log(x*E)/log(2)/cos(2*x)
The first derivative
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___ ___
/ _________\ 1 5*\/ 5 *\/ x 2*log(x*E)*sin(2*x)
10*acos\\/ 1 - 5*x / - ----------------- + ------------- - -------------------
x*cos(2*x)*log(2) _________ 2
\/ 1 - 5*x cos (2*x)*log(2)
$$\frac{5 \sqrt{5} \sqrt{x}}{\sqrt{1 - 5 x}} - \frac{2 \log{\left(e x \right)} \sin{\left(2 x \right)}}{\log{\left(2 \right)} \cos^{2}{\left(2 x \right)}} + 10 \operatorname{acos}{\left(\sqrt{1 - 5 x} \right)} - \frac{1}{x \log{\left(2 \right)} \cos{\left(2 x \right)}}$$
The second derivative
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___ ___ ___ 2
1 4*log(E*x) 15*\/ 5 25*\/ 5 *\/ x 8*sin (2*x)*log(E*x) 4*sin(2*x)
------------------ - --------------- + ------------------- + -------------- - -------------------- - ------------------
2 cos(2*x)*log(2) ___ _________ 3/2 3 2
x *cos(2*x)*log(2) 2*\/ x *\/ 1 - 5*x 2*(1 - 5*x) cos (2*x)*log(2) x*cos (2*x)*log(2)
$$\frac{25 \sqrt{5} \sqrt{x}}{2 \left(1 - 5 x\right)^{\frac{3}{2}}} - \frac{8 \log{\left(e x \right)} \sin^{2}{\left(2 x \right)}}{\log{\left(2 \right)} \cos^{3}{\left(2 x \right)}} - \frac{4 \log{\left(e x \right)}}{\log{\left(2 \right)} \cos{\left(2 x \right)}} - \frac{4 \sin{\left(2 x \right)}}{x \log{\left(2 \right)} \cos^{2}{\left(2 x \right)}} + \frac{1}{x^{2} \log{\left(2 \right)} \cos{\left(2 x \right)}} + \frac{15 \sqrt{5}}{2 \sqrt{x} \sqrt{1 - 5 x}}$$
The third derivative
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___ ___ ___ ___ 3 2
12 2 25*\/ 5 15*\/ 5 375*\/ 5 *\/ x 48*sin (2*x)*log(E*x) 40*log(E*x)*sin(2*x) 24*sin (2*x) 6*sin(2*x)
- ----------------- - ------------------ + ------------------ - ------------------ + --------------- - --------------------- - -------------------- - ------------------ + -------------------
x*cos(2*x)*log(2) 3 ___ 3/2 3/2 _________ 5/2 4 2 3 2 2
x *cos(2*x)*log(2) \/ x *(1 - 5*x) 4*x *\/ 1 - 5*x 4*(1 - 5*x) cos (2*x)*log(2) cos (2*x)*log(2) x*cos (2*x)*log(2) x *cos (2*x)*log(2)
$$\frac{375 \sqrt{5} \sqrt{x}}{4 \left(1 - 5 x\right)^{\frac{5}{2}}} - \frac{48 \log{\left(e x \right)} \sin^{3}{\left(2 x \right)}}{\log{\left(2 \right)} \cos^{4}{\left(2 x \right)}} - \frac{40 \log{\left(e x \right)} \sin{\left(2 x \right)}}{\log{\left(2 \right)} \cos^{2}{\left(2 x \right)}} - \frac{24 \sin^{2}{\left(2 x \right)}}{x \log{\left(2 \right)} \cos^{3}{\left(2 x \right)}} - \frac{12}{x \log{\left(2 \right)} \cos{\left(2 x \right)}} + \frac{6 \sin{\left(2 x \right)}}{x^{2} \log{\left(2 \right)} \cos^{2}{\left(2 x \right)}} - \frac{2}{x^{3} \log{\left(2 \right)} \cos{\left(2 x \right)}} + \frac{25 \sqrt{5}}{\sqrt{x} \left(1 - 5 x\right)^{\frac{3}{2}}} - \frac{15 \sqrt{5}}{4 x^{\frac{3}{2}} \sqrt{1 - 5 x}}$$