Step 1:

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

[latex]\large{\frac{dy}{dx} = 7(5)x^{5-1}-2(4)x^{4-1}+3(2)x^{2-1}}[/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{\frac{dy}{dx} = 35x^4-8x^3+6x}[/latex]

This is the first derivative.

We are not done yet since we need to find [latex]\frac{d^2y}{dx^2}[/latex] which is the second derivative.

Step 3:

Thus, using the power rule once more, we have:

[latex]\large{\frac{d^2y}{dx^2} = 35(4)x^{4-1}-8(3)x^{3-1}+6(1)x^{1-1}}[/latex]

[latex]\large{\frac{d^2y}{dx^2} = 140x^3 – 24x^2 + 6}[/latex]

Solution Complete!