Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of (x^2-x)*(x^3+x)
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Derivative of (x^2-1)*(x^4+2)
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Derivative of log
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Derivative of log(e)
- Integral of d{x}:
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cos(1/x)
- Graphing y =:
- cos(1/x)
- Limit of the function:
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cos(1/x)
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Identical expressions
- cos(one /x)
- co sinus of e of (1 divide by x)
- co sinus of e of (one divide by x)
- cos1/x
- cos(1 divide by x)
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Similar expressions
- (8*acot(5)^9*x+3*acos(1/(x^5)))/(((9*x^9+9*x^5)^(1/5)*(-5)))
- x^2*cos(1)/x
- ((x^4*log(2*x-4^sqrt(x)))/(sin(8*x^2+4)^(3)))+acos(1)/x
Derivative of cos(1/x)
The solution
Detail solution
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Let .
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The derivative of cosine is negative sine:
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Then, apply the chain rule. Multiply by :
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Apply the power rule: goes to
The result of the chain rule is:
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The answer is:
The first derivative
[src]
/1\ sin|-| \x/ ------ 2 x
$$\frac{\sin{\left(\frac{1}{x} \right)}}{x^{2}}$$
The second derivative
[src]
/ /1\\
| cos|-||
| /1\ \x/|
-|2*sin|-| + ------|
\ \x/ x /
---------------------
3
x
$$- \frac{2 \sin{\left(\frac{1}{x} \right)} + \frac{\cos{\left(\frac{1}{x} \right)}}{x}}{x^{3}}$$
The third derivative
[src]
/1\ /1\
sin|-| 6*cos|-|
/1\ \x/ \x/
6*sin|-| - ------ + --------
\x/ 2 x
x
----------------------------
4
x
$$\frac{6 \sin{\left(\frac{1}{x} \right)} + \frac{6 \cos{\left(\frac{1}{x} \right)}}{x} - \frac{\sin{\left(\frac{1}{x} \right)}}{x^{2}}}{x^{4}}$$
The graph