Derivative of 3x^2sinx

1. The derivative of a constant times a function is the constant times the derivative of the function.

   1. Apply the product rule:

      $$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$$

      $f{\left(x \right)} = x^{2}$; to find $\frac{d}{d x} f{\left(x \right)}$:

      1. Apply the power rule: $x^{2}$ goes to $2 x$

      $g{\left(x \right)} = \sin{\left(x \right)}$; to find $\frac{d}{d x} g{\left(x \right)}$:

      1. The derivative of sine is cosine:

         $$\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$$

      The result is: $x^{2} \cos{\left(x \right)} + 2 x \sin{\left(x \right)}$

   So, the result is: $3 x^{2} \cos{\left(x \right)} + 6 x \sin{\left(x \right)}$

2. Now simplify:

   $$3 x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)$$

The answer is: