Question

hw_2.1_basic derivative rules
due sunday by 11:59pm points 100.05
hw_2.1_basic derivative rules

1. submit answer practice similar

attempt 1: 10 attempts remaining.
differentiate the following function:
f(x)=x^{2}-6x - 37
f(x)=

Explanation:

Step1: Apply power - rule to $x^2$

The power - rule states that if $y = x^n$, then $y^\prime=nx^{n - 1}$. For $y=x^2$, $y^\prime = 2x^{2-1}=2x$.

Step2: Apply power - rule to $-6x$

For $y=-6x=-6x^1$, using the power - rule $y^\prime=-6\times1\times x^{1 - 1}=-6$.

Step3: Apply rule for constant

The derivative of a constant $C$ is $0$. For $y = - 37$, $y^\prime=0$.

Step4: Combine the derivatives

Since $f(x)=x^2-6x - 37$, then $f^\prime(x)$ is the sum of the derivatives of each term. So $f^\prime(x)=2x-6+0$.

Answer:

$2x - 6$