Question

find the derivative of the function.
y = x^3 - \frac{x^2}{8}+x + 5
y = square

Explanation:

Step1: Apply power - rule to each term

The power - rule states that if $y = ax^n$, then $y'=nax^{n - 1}$. For the term $x^3$, $n = 3$ and $a = 1$, so its derivative is $3x^{3-1}=3x^2$. For the term $-\frac{x^2}{8}$, $n = 2$ and $a=-\frac{1}{8}$, so its derivative is $2\times(-\frac{1}{8})x^{2 - 1}=-\frac{1}{4}x$. For the term $x$, $n = 1$ and $a = 1$, so its derivative is $1\times x^{1-1}=1$. For the constant term $5$, the derivative of a constant is $0$.

Step2: Combine the derivatives of each term

$y'=3x^2-\frac{1}{4}x + 1+0$.

Answer:

$3x^2-\frac{1}{4}x + 1$