Find the derivative. y=x^2+9x+4 y'=square

To find the derivative of the function \( y = x^2 + 9x + 4 \), we will differentiate each term with respect to \( x \).<br /><br />The power rule states that the derivative of \( x^n \) is \( nx^{n-1} \).<br /><br />1. Differentiate \( x^2 \):<br /> \[<br /> \frac{d}{dx}(x^2) = 2x<br /> \]<br /><br />2. Differentiate \( 9x \):<br /> \[<br /> \frac{d}{dx}(9x) = 9<br /> \]<br /><br />3. The derivative of the constant term \( 4 \) is \( 0 \):<br /> \[<br /> \frac{d}{dx}(4) = 0<br /> \]<br /><br />Now, combine these results:<br />\[<br />y' = 2x + 9<br />\]<br /><br />So, the derivative of \( y = x^2 + 9x + 4 \) is:<br />\[<br />y' = 2x + 9<br />\]