Find the derivative of the function. $$ y=5 x^{2}-3 x-3 x^{-2} $$ $$ \frac{d y}{d x}=\square $$

Question

UpStudy AI · Accepted Answer

To find the derivative of the function $$ y = 5x^2 - 3x - 3x^{-2} $$, we will differentiate each term separately.

1. The derivative of $$ 5x^2 $$ is:
   $$
   \frac{d}{dx}(5x^2) = 10x
   $$

2. The derivative of $$ -3x $$ is:
   $$
   \frac{d}{dx}(-3x) = -3
   $$

3. The derivative of $$ -3x^{-2} $$ is:
   $$
   \frac{d}{dx}(-3x^{-2}) = -3 \cdot (-2)x^{-3} = 6x^{-3}
   $$

Now, we can combine these results to find the derivative $$ \frac{dy}{dx} $$:
$$
\frac{dy}{dx} = 10x - 3 + 6x^{-3}
$$

Thus, the final answer is:
$$
\frac{dy}{dx} = 10x - 3 + \frac{6}{x^3}
$$
$$ \frac{dy}{dx} = 10x - 3 + \frac{6}{x^3} $$

Find the derivative of the function.