Derivative of x*sqrt4(x)+3sin1

1. Differentiate $x^{0.25} x + 3 \sin{\left(1 \right)}$ term by term:

   1. Apply the product rule:

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

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

      1. Apply the power rule: $x$ goes to $1$

      $g{\left(x \right)} = x^{0.25}$; to find $\frac{d}{d x} g{\left(x \right)}$:

      1. Apply the power rule: $x^{0.25}$ goes to $\frac{0.25}{x^{0.75}}$

      The result is: $1.25 x^{0.25}$

   2. The derivative of the constant $3 \sin{\left(1 \right)}$ is zero.

   The result is: $1.25 x^{0.25}$

The answer is:

$$1.25 x^{0.25}$$