Question

question 20 · 1 point
find the derivative of f(x)=3x^4 - 7x + 1.
provide your answer below:
f(x)=□

Explanation:

Step1: Apply power - rule to $3x^{4}$

The power - rule states that if $y = ax^{n}$, then $y'=nax^{n - 1}$. For $y = 3x^{4}$, $n = 4$ and $a = 3$. So the derivative is $4\times3x^{4 - 1}=12x^{3}$.

Step2: Apply power - rule to $-7x$

For $y=-7x$, $n = 1$ and $a=-7$. Using the power - rule $y'=1\times(-7)x^{1 - 1}=-7$.

Step3: Derivative of constant

The derivative of a constant $C$ (in this case $C = 1$) is $0$.

Step4: Combine derivatives

$f'(x)$ is the sum of the derivatives of each term. So $f'(x)=12x^{3}-7 + 0=12x^{3}-7$.

Answer:

$12x^{3}-7$