Detail solution
-
Apply the product rule:
; to find :
-
Apply the power rule: goes to
; to find :
-
The derivative of cosine is negative sine:
The result is:
-
Now simplify:
The answer is:
The first derivative
[src]
2
- x *sin(x) + 2*x*cos(x)
$$- x^{2} \sin{\left(x \right)} + 2 x \cos{\left(x \right)}$$
The second derivative
[src]
2
2*cos(x) - x *cos(x) - 4*x*sin(x)
$$- x^{2} \cos{\left(x \right)} - 4 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}$$
The third derivative
[src]
2
-6*sin(x) + x *sin(x) - 6*x*cos(x)
$$x^{2} \sin{\left(x \right)} - 6 x \cos{\left(x \right)} - 6 \sin{\left(x \right)}$$