Derivative of y=4x^2+lnx-sinx

1. Differentiate $\left(4 x^{2} + \log{\left(x \right)}\right) - \sin{\left(x \right)}$ term by term:

   1. Differentiate $4 x^{2} + \log{\left(x \right)}$ term by term:

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

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

         So, the result is: $8 x$

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

      The result is: $8 x + \frac{1}{x}$

   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: $8 x - \cos{\left(x \right)} + \frac{1}{x}$

The answer is:

$$8 x - \cos{\left(x \right)} + \frac{1}{x}$$