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
-
How to use it?
- Derivative of:
-
Derivative of tanh(x)
-
Derivative of tanx
-
Derivative of tg2x
-
Derivative of y=9
-
Identical expressions
- (log2(x))^cosx
- ( logarithm of 2(x)) to the power of co sinus of e of x
- (log2(x))cosx
- log2xcosx
- log2x^cosx
-
Similar expressions
- (log2*x)^(cosx^2)
Derivative of (log2(x))^cosx
The solution
You have entered
[src]
cos(x) /log(x)\ |------| \log(2)/
$$\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cos{\left(x \right)}}$$
(log(x)/log(2))^cos(x)
Detail solution
-
Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
cos(x) /log(x)\ / /log(x)\ cos(x) \ |------| *|- log|------|*sin(x) + --------| \log(2)/ \ \log(2)/ x*log(x)/
$$\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cos{\left(x \right)}} \left(- \log{\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x \log{\left(x \right)}}\right)$$
The second derivative
[src]
cos(x) / 2 \
/log(x)\ |/ /log(x)\ cos(x) \ /log(x)\ cos(x) cos(x) 2*sin(x)|
|------| *||log|------|*sin(x) - --------| - cos(x)*log|------| - --------- - ---------- - --------|
\log(2)/ |\ \log(2)/ x*log(x)/ \log(2)/ 2 2 2 x*log(x)|
\ x *log(x) x *log (x) /
$$\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cos{\left(x \right)}} \left(\left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x \log{\left(x \right)}}\right)^{2} - \log{\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x \log{\left(x \right)}} - \frac{\cos{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\cos{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right)$$
The third derivative
[src]
cos(x) / 3 \
/log(x)\ | / /log(x)\ cos(x) \ /log(x)\ / /log(x)\ cos(x) \ / /log(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|------|*sin(x) - --------| + log|------|*sin(x) + 3*|log|------|*sin(x) - --------|*|cos(x)*log|------| + --------- + ---------- + --------| - -------- + --------- + ---------- + ---------- + --------- + ----------|
\log(2)/ | \ \log(2)/ x*log(x)/ \log(2)/ \ \log(2)/ x*log(x)/ | \log(2)/ 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)/
$$\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cos{\left(x \right)}} \left(- \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x \log{\left(x \right)}}\right)^{3} + 3 \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x \log{\left(x \right)}}\right) \left(\log{\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x \log{\left(x \right)}} + \frac{\cos{\left(x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\cos{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) + \log{\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x \log{\left(x \right)}} + \frac{3 \sin{\left(x \right)}}{x^{2} \log{\left(x \right)}} + \frac{3 \sin{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \cos{\left(x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right)$$