Step 1:

First, we will remove the fraction, by rewriting the function as follows:

[latex]\large{y = 3x^4-5x^{-3}+2x^2+3}[/latex]

Notice that we can now use the derivative power rule to find the derivative.

Step 2:

Applying the power rule, we have:

[latex]\large{\frac{dy}{dx} = (3)x^{4-1} – 5(-3)x^{-3-1} + 2(2)x^{2-1}}[/latex]

[latex]\large{\frac{dy}{dx} = 3x^3 +15x^{-4}+4x}[/latex]

Notice how we brought the exponent down and subtracted the exponent by 1.

Thus, we have:

[latex]\large{\frac{dy}{dx} = 3x^3 + \frac{15}{x^4} + 4x}[/latex]

This is our final answer for the derivative.

Solution Complete!