Detail solution
-
Apply the product rule:
; to find :
-
The derivative of cosine is negative sine:
; to find :
-
The derivative of is .
The result is:
The answer is:
The first derivative
[src]
cos(x)
------ - log(x)*sin(x)
x
$$- \log{\left(x \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}$$
The second derivative
[src]
/cos(x) 2*sin(x)\
-|------ + cos(x)*log(x) + --------|
| 2 x |
\ x /
$$- (\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}})$$
The third derivative
[src]
3*cos(x) 2*cos(x) 3*sin(x)
log(x)*sin(x) - -------- + -------- + --------
x 3 2
x x
$$\log{\left(x \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x} + \frac{3 \sin{\left(x \right)}}{x^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3}}$$