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How to use it?
- Derivative of:
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Derivative of tan(x/2)
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Derivative of (x^2)
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Derivative of sin(x)/2
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Derivative of lnx
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Identical expressions
- arcsin five x*sinx*((x^5)+ one)^ three
- arc sinus of 5x multiply by sinus of x multiply by ((x to the power of 5) plus 1) cubed
- arc sinus of five x multiply by sinus of x multiply by ((x to the power of 5) plus one) to the power of three
- arcsin5x*sinx*((x5)+1)3
- arcsin5x*sinx*x5+13
- arcsin5x*sinx*((x⁵)+1)³
- arcsin5x*sinx*((x to the power of 5)+1) to the power of 3
- arcsin5xsinx((x^5)+1)^3
- arcsin5xsinx((x5)+1)3
- arcsin5xsinxx5+13
- arcsin5xsinxx^5+1^3
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Similar expressions
- arcsin5x*sinx*((x^5)-1)^3
Derivative of arcsin5x*sinx*((x^5)+1)^3
The solution
You have entered
[src]
3
/ 5 \
asin(5*x)*sin(x)*\x + 1/
$$\sin{\left(x \right)} \operatorname{asin}{\left(5 x \right)} \left(x^{5} + 1\right)^{3}$$
(asin(5*x)*sin(x))*(x^5 + 1)^3
The first derivative
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3 2
/ 5 \ / 5*sin(x) \ 4 / 5 \
\x + 1/ *|asin(5*x)*cos(x) + --------------| + 15*x *\x + 1/ *asin(5*x)*sin(x)
| ___________|
| / 2 |
\ \/ 1 - 25*x /
$$15 x^{4} \left(x^{5} + 1\right)^{2} \sin{\left(x \right)} \operatorname{asin}{\left(5 x \right)} + \left(x^{5} + 1\right)^{3} \left(\cos{\left(x \right)} \operatorname{asin}{\left(5 x \right)} + \frac{5 \sin{\left(x \right)}}{\sqrt{1 - 25 x^{2}}}\right)$$
The second derivative
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/ 2 \
/ 5\ |/ 5\ / 10*cos(x) 125*x*sin(x) \ 4 / 5\ / 5*sin(x) \ 3 / 5\ |
\1 + x /*|\1 + x / *|-asin(5*x)*sin(x) + -------------- + --------------| + 30*x *\1 + x /*|asin(5*x)*cos(x) + --------------| + 30*x *\2 + 7*x /*asin(5*x)*sin(x)|
| | ___________ 3/2| | ___________| |
| | / 2 / 2\ | | / 2 | |
\ \ \/ 1 - 25*x \1 - 25*x / / \ \/ 1 - 25*x / /
$$\left(x^{5} + 1\right) \left(30 x^{4} \left(x^{5} + 1\right) \left(\cos{\left(x \right)} \operatorname{asin}{\left(5 x \right)} + \frac{5 \sin{\left(x \right)}}{\sqrt{1 - 25 x^{2}}}\right) + 30 x^{3} \left(7 x^{5} + 2\right) \sin{\left(x \right)} \operatorname{asin}{\left(5 x \right)} + \left(x^{5} + 1\right)^{2} \left(\frac{125 x \sin{\left(x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \sin{\left(x \right)} \operatorname{asin}{\left(5 x \right)} + \frac{10 \cos{\left(x \right)}}{\sqrt{1 - 25 x^{2}}}\right)\right)$$
The third derivative
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/ / 2 \ \
| | 75*x | |
| 125*|-1 + ----------|*sin(x)|
3 | | 2| | 2 / 2 \
/ 5\ | 15*sin(x) 375*x*cos(x) \ -1 + 25*x / | 4 / 5\ / 10*cos(x) 125*x*sin(x) \ 2 | / 5\ 10 5 / 5\| 3 / 5\ / 5\ / 5*sin(x) \
- \1 + x / *|asin(5*x)*cos(x) + -------------- - -------------- + ----------------------------| + 45*x *\1 + x / *|-asin(5*x)*sin(x) + -------------- + --------------| + 30*x *\6*\1 + x / + 25*x + 60*x *\1 + x //*asin(5*x)*sin(x) + 90*x *\1 + x /*\2 + 7*x /*|asin(5*x)*cos(x) + --------------|
| ___________ 3/2 3/2 | | ___________ 3/2| | ___________|
| / 2 / 2\ / 2\ | | / 2 / 2\ | | / 2 |
\ \/ 1 - 25*x \1 - 25*x / \1 - 25*x / / \ \/ 1 - 25*x \1 - 25*x / / \ \/ 1 - 25*x /
$$45 x^{4} \left(x^{5} + 1\right)^{2} \left(\frac{125 x \sin{\left(x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \sin{\left(x \right)} \operatorname{asin}{\left(5 x \right)} + \frac{10 \cos{\left(x \right)}}{\sqrt{1 - 25 x^{2}}}\right) + 90 x^{3} \left(x^{5} + 1\right) \left(7 x^{5} + 2\right) \left(\cos{\left(x \right)} \operatorname{asin}{\left(5 x \right)} + \frac{5 \sin{\left(x \right)}}{\sqrt{1 - 25 x^{2}}}\right) + 30 x^{2} \left(25 x^{10} + 60 x^{5} \left(x^{5} + 1\right) + 6 \left(x^{5} + 1\right)^{2}\right) \sin{\left(x \right)} \operatorname{asin}{\left(5 x \right)} - \left(x^{5} + 1\right)^{3} \left(- \frac{375 x \cos{\left(x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \cos{\left(x \right)} \operatorname{asin}{\left(5 x \right)} + \frac{15 \sin{\left(x \right)}}{\sqrt{1 - 25 x^{2}}} + \frac{125 \left(\frac{75 x^{2}}{25 x^{2} - 1} - 1\right) \sin{\left(x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}\right)$$