Question

find the derivative of the function. y = x^3 - 7x^2 + 16x + 9 y = □

Explanation:

Step1: Apply power - rule for each term

The power - rule states that if $y = ax^n$, then $y'=nax^{n - 1}$. For the term $x^3$, using the power - rule: $\frac{d}{dx}(x^3)=3x^{3 - 1}=3x^2$. For the term $-7x^2$, $\frac{d}{dx}(-7x^2)=-7\times2x^{2 - 1}=-14x$. For the term $16x$, $\frac{d}{dx}(16x)=16\times1x^{1 - 1}=16$. For the constant term $9$, $\frac{d}{dx}(9) = 0$ since the derivative of a constant is 0.

Step2: Combine the derivatives of each term

$y'=\frac{d}{dx}(x^3)-\frac{d}{dx}(7x^2)+\frac{d}{dx}(16x)+\frac{d}{dx}(9)=3x^2-14x + 16+0$.

Answer:

$3x^2-14x + 16$