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- Derivative of:
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Derivative of sin(x)/cos(x)
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Derivative of cos(x)^(3)
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Derivative of tan(x^3)
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Derivative of 1/(2*sqrt(x))
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Identical expressions
- (e^arccos(x))/x+ five
- (e to the power of arc co sinus of e of (x)) divide by x plus 5
- (e to the power of arc co sinus of e of (x)) divide by x plus five
- (earccos(x))/x+5
- earccosx/x+5
- e^arccosx/x+5
- (e^arccos(x)) divide by x+5
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Similar expressions
- (e^arccos(x))/x-5
- (e^arccosx)/x+5
Derivative of (e^arccos(x))/x+5
The solution
You have entered
[src]
acos(x) E -------- + 5 x
$$\frac{e^{\operatorname{acos}{\left(x \right)}}}{x} + 5$$
E^acos(x)/x + 5
The first derivative
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acos(x) acos(x)
e e
- -------- - -------------
2 ________
x / 2
x*\/ 1 - x
$$- \frac{e^{\operatorname{acos}{\left(x \right)}}}{x \sqrt{1 - x^{2}}} - \frac{e^{\operatorname{acos}{\left(x \right)}}}{x^{2}}$$
The second derivative
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/ 1 2 1 2 \ acos(x) |- ----------- + -- - ----------- + --------------|*e | 3/2 3 / 2\ ________| | / 2\ x x*\-1 + x / 2 / 2 | \ \1 - x / x *\/ 1 - x /
$$\left(- \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x \left(x^{2} - 1\right)} + \frac{2}{x^{2} \sqrt{1 - x^{2}}} + \frac{2}{x^{3}}\right) e^{\operatorname{acos}{\left(x \right)}}$$
The third derivative
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/ 6 3 1 6 3*x 3 \ acos(x) |- -- + ---------- + ------------- - -------------- - ----------- + ------------|*e | 4 2 3/2 ________ 5/2 2 / 2\| | x / 2\ / 2\ 3 / 2 / 2\ x *\-1 + x /| \ \-1 + x / x*\1 - x / x *\/ 1 - x \1 - x / /
$$\left(- \frac{3 x}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3}{\left(x^{2} - 1\right)^{2}} + \frac{1}{x \left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{x^{2} \left(x^{2} - 1\right)} - \frac{6}{x^{3} \sqrt{1 - x^{2}}} - \frac{6}{x^{4}}\right) e^{\operatorname{acos}{\left(x \right)}}$$