Derivative of y=x^3-sinx+lnx

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

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

      1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

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

         1. The derivative of sine is cosine:

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

         So, the result is: $- \cos{\left(x \right)}$

      The result is: $3 x^{2} - \cos{\left(x \right)}$

   2. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$.

   The result is: $3 x^{2} - \cos{\left(x \right)} + \frac{1}{x}$

The answer is:

$$3 x^{2} - \cos{\left(x \right)} + \frac{1}{x}$$