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