Step 1:

We can use the derivative power rule to find the derivative of the given function. We have:

[latex]\large{f'(x) = 5(3)x^{3-1}+2(2)x^{2-1}-7(1)x^{1-1}}[/latex]

Notice that we brought down the exponent, and subtracted the exponent by 1 for each term.

Step 2:

Now, after simplifying, we have:

[latex]\large{f'(x) = 15x^2+4x-7}[/latex]

This is our final answer for the derivative.

Solution Complete!