Detail solution
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Apply the product rule:
; to find :
-
Apply the power rule: goes to
; to find :
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The derivative of cosine is negative sine:
The result is:
-
Now simplify:
The answer is:
The first derivative
[src]
3 2
- x *sin(x) + 3*x *cos(x)
$$- x^{3} \sin{\left(x \right)} + 3 x^{2} \cos{\left(x \right)}$$
The second derivative
[src]
/ 2 \
x*\6*cos(x) - x *cos(x) - 6*x*sin(x)/
$$x \left(- x^{2} \cos{\left(x \right)} - 6 x \sin{\left(x \right)} + 6 \cos{\left(x \right)}\right)$$
The third derivative
[src]
3 2
6*cos(x) + x *sin(x) - 18*x*sin(x) - 9*x *cos(x)
$$x^{3} \sin{\left(x \right)} - 9 x^{2} \cos{\left(x \right)} - 18 x \sin{\left(x \right)} + 6 \cos{\left(x \right)}$$