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
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Derivative of log(x)/x
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Derivative of x²-4x
- Derivative of cos^3(7x)
- Graphing y =:
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log(x)/x
- Limit of the function:
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log(x)/x
- Integral of d{x}:
- log(x)/x
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Identical expressions
- log(x)/x
- logarithm of (x) divide by x
- logx/x
- log(x) divide by x
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Similar expressions
- (1-log(x))/x^2
- f(x)=10logx/x
- sin(log(x))/x
- y=sin(logx)-cos(logx)/x
Derivative of log(x)/x
The solution
You have entered
[src]
log(x) ------ x
$$\frac{\log{\left(x \right)}}{x}$$
d /log(x)\ --|------| dx\ x /
$$\frac{d}{d x} \frac{\log{\left(x \right)}}{x}$$
Detail solution
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Apply the quotient rule, which is:
and .
To find :
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The derivative of is .
To find :
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Apply the power rule: goes to
Now plug in to the quotient rule:
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The answer is:
The first derivative
[src]
1 log(x) -- - ------ 2 2 x x
$$- \frac{\log{\left(x \right)}}{x^{2}} + \frac{1}{x^{2}}$$
The second derivative
[src]
-3 + 2*log(x)
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3
x
$$\frac{2 \log{\left(x \right)} - 3}{x^{3}}$$
The third derivative
[src]
11 - 6*log(x)
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4
x
$$\frac{11 - 6 \log{\left(x \right)}}{x^{4}}$$
The graph