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 sin(x)^2
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Derivative of x^-6
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Derivative of ex^2
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Derivative of e^sin(x)*cos(x)
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Identical expressions
- (log(x))^(cos(x))
- ( logarithm of (x)) to the power of ( co sinus of e of (x))
- (log(x))(cos(x))
- logxcosx
- logx^cosx
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Similar expressions
- (log(x))^(cosx)
Derivative of (log(x))^(cos(x))
The solution
You have entered
[src]
cos(x) log (x)
$$\log{\left(x \right)}^{\cos{\left(x \right)}}$$
log(x)^cos(x)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
cos(x) / cos(x) \
log (x)*|-log(log(x))*sin(x) + --------|
\ x*log(x)/
$$\left(- \log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\cos{\left(x \right)}}$$
The second derivative
[src]
/ 2 \
cos(x) |/ cos(x) \ cos(x) cos(x) 2*sin(x)|
log (x)*||log(log(x))*sin(x) - --------| - cos(x)*log(log(x)) - --------- - ---------- - --------|
|\ x*log(x)/ 2 2 2 x*log(x)|
\ x *log(x) x *log (x) /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x \log{\left(x \right)}}\right)^{2} - \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x \log{\left(x \right)}} - \frac{\cos{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\cos{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\cos{\left(x \right)}}$$
The third derivative
[src]
/ 3 \
cos(x) | / cos(x) \ / cos(x) \ / cos(x) cos(x) 2*sin(x)\ 3*cos(x) 2*cos(x) 2*cos(x) 3*cos(x) 3*sin(x) 3*sin(x) |
log (x)*|- |log(log(x))*sin(x) - --------| + log(log(x))*sin(x) + 3*|log(log(x))*sin(x) - --------|*|cos(x)*log(log(x)) + --------- + ---------- + --------| - -------- + --------- + ---------- + ---------- + --------- + ----------|
| \ x*log(x)/ \ x*log(x)/ | 2 2 2 x*log(x)| x*log(x) 3 3 3 3 2 2 2 2 |
\ \ x *log(x) x *log (x) / x *log(x) x *log (x) x *log (x) x *log(x) x *log (x)/
$$\left(- \left(\log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x \log{\left(x \right)}}\right)^{3} + 3 \left(\log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x \log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x \log{\left(x \right)}} + \frac{\cos{\left(x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\cos{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) + \log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x \log{\left(x \right)}} + \frac{3 \sin{\left(x \right)}}{x^{2} \log{\left(x \right)}} + \frac{3 \sin{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \cos{\left(x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\cos{\left(x \right)}}$$