Question

hw10 differentiation rules 1 (targets c1, c5; §3.3)
score: 1/9 answered: 1/9
question 2
if (f(x)=5x^{2}-6x - 8), find (f(x)).
question help: video message instructor

Explanation:

Step1: Apply power - rule to first term

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the term $5x^2$, $a = 5$ and $n = 2$. So the derivative of $5x^2$ is $2\times5x^{2 - 1}=10x$.

Step2: Apply power - rule to second term

For the term $-6x$, $a=-6$ and $n = 1$. Using the power - rule, the derivative of $-6x$ is $1\times(-6)x^{1 - 1}=-6$.

Step3: Apply rule for constant term

The derivative of a constant $c$ is 0. For the term $-8$ (where $c=-8$), its derivative is 0.

Step4: Combine the derivatives

$f^\prime(x)$ is the sum of the derivatives of each term. So $f^\prime(x)=10x-6 + 0=10x-6$.

Answer:

$10x - 6$