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