Mister Exam
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- 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 2x²
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Derivative of f(x)=1
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Derivative of e^x*x^2
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Derivative of 2*sqrt(x^3)
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Identical expressions
- y= two (x/lnx)
- y equally 2(x divide by lnx)
- y equally two (x divide by lnx)
- y=2x/lnx
- y=2(x divide by lnx)
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Similar expressions
- y=(sin^2x)/(ln(x^2+1))
- 2^(x/lnx)
- 2^(x/ln(x))
- 2x/ln(x)
Derivative of y=2(x/lnx)
The solution
You have entered
[src]
2*x ------ log(x)
$$\frac{2 x}{\log{\left(x \right)}}$$
d / 2*x \ --|------| dx\log(x)/
$$\frac{d}{d x} \frac{2 x}{\log{\left(x \right)}}$$
Detail solution
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The derivative of a constant times a function is the constant times the derivative of the function.
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Apply the quotient rule, which is:
and .
To find :
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Apply the power rule: goes to
To find :
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The derivative of is .
Now plug in to the quotient rule:
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So, the result is:
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The answer is:
The first derivative
[src]
2 2
- ------- + ------
2 log(x)
log (x)
$$\frac{2}{\log{\left(x \right)}} - \frac{2}{\log{\left(x \right)}^{2}}$$
The second derivative
[src]
/ 2 \
2*|-1 + ------|
\ log(x)/
---------------
2
x*log (x)
$$\frac{2 \left(-1 + \frac{2}{\log{\left(x \right)}}\right)}{x \log{\left(x \right)}^{2}}$$
The third derivative
[src]
/ 6 \
2*|1 - -------|
| 2 |
\ log (x)/
---------------
2 2
x *log (x)
$$\frac{2 \cdot \left(1 - \frac{6}{\log{\left(x \right)}^{2}}\right)}{x^{2} \log{\left(x \right)}^{2}}$$
3-я производная
[src]
/ 6 \
2*|1 - -------|
| 2 |
\ log (x)/
---------------
2 2
x *log (x)
$$\frac{2 \cdot \left(1 - \frac{6}{\log{\left(x \right)}^{2}}\right)}{x^{2} \log{\left(x \right)}^{2}}$$
The graph