Question

question find the derivative of f(x)=2x^7 - x^3. provide your answer below: f(x)=□

Explanation:

Step1: Recall power - rule for derivatives

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

Step2: Differentiate each term of $f(x)$

For the first term $y_1 = 2x^7$, using the power - rule, $y_1^\prime=2\times7x^{7 - 1}=14x^6$. For the second term $y_2=-x^3$, using the power - rule, $y_2^\prime=-3x^{3 - 1}=-3x^2$.

Step3: Combine the derivatives of the terms

Since $f(x)=2x^7 - x^3$, then $f^\prime(x)=y_1^\prime + y_2^\prime$. So $f^\prime(x)=14x^6-3x^2$.

Answer:

$14x^6 - 3x^2$