3 x *sin(x)
d / 3 \ --\x *sin(x)/ dx
Apply the product rule:
f(x)=x3f{\left(x \right)} = x^{3}f(x)=x3; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}dxdf(x):
Apply the power rule: x3x^{3}x3 goes to 3x23 x^{2}3x2
g(x)=sin(x)g{\left(x \right)} = \sin{\left(x \right)}g(x)=sin(x); to find ddxg(x)\frac{d}{d x} g{\left(x \right)}dxdg(x):
The derivative of sine is cosine:
The result is: x3cos(x)+3x2sin(x)x^{3} \cos{\left(x \right)} + 3 x^{2} \sin{\left(x \right)}x3cos(x)+3x2sin(x)
Now simplify:
The answer is:
3 2 x *cos(x) + 3*x *sin(x)
/ 2 \ x*\6*sin(x) - x *sin(x) + 6*x*cos(x)/
3 2 6*sin(x) - x *cos(x) - 9*x *sin(x) + 18*x*cos(x)