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 x^(1/4)
-
Derivative of -sin(x)
-
Derivative of sin(sqrt(x))
-
Derivative of sin(4*x)
-
Identical expressions
- (cos(x))^x
- ( co sinus of e of (x)) to the power of x
- (cos(x))x
- cosxx
- cosx^x
-
Similar expressions
- y=(1+cosx)^x^5
- (cosx)^x
Derivative of (cos(x))^x
The solution
You have entered
[src]
x cos (x)
$$\cos^{x}{\left(x \right)}$$
d / x \ --\cos (x)/ dx
$$\frac{d}{d x} \cos^{x}{\left(x \right)}$$
Detail solution
-
Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
x / x*sin(x) \
cos (x)*|- -------- + log(cos(x))|
\ cos(x) /
$$\left(- \frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} + \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{x}{\left(x \right)}$$
The second derivative
[src]
/ 2 2 \
x |/ x*sin(x)\ 2*sin(x) x*sin (x)|
cos (x)*||-log(cos(x)) + --------| - x - -------- - ---------|
|\ cos(x) / cos(x) 2 |
\ cos (x) /
$$\left(\left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(\cos{\left(x \right)} \right)}\right)^{2} - \frac{x \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - x - \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \cos^{x}{\left(x \right)}$$
The third derivative
[src]
/ 3 2 / 2 \ 3 \
x | / x*sin(x)\ 3*sin (x) / x*sin(x)\ | 2*sin(x) x*sin (x)| 2*x*sin(x) 2*x*sin (x)|
cos (x)*|-3 - |-log(cos(x)) + --------| - --------- + 3*|-log(cos(x)) + --------|*|x + -------- + ---------| - ---------- - -----------|
| \ cos(x) / 2 \ cos(x) / | cos(x) 2 | cos(x) 3 |
\ cos (x) \ cos (x) / cos (x) /
$$\left(- \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(\cos{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(\cos{\left(x \right)} \right)}\right) \left(\frac{x \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + x + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) - \frac{2 x \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 3\right) \cos^{x}{\left(x \right)}$$
The graph