timed problem score: 1/10 current time: 24.4 $\frac{d}{dx}(4x^{-5})$ answer $-\frac{2}{3}x^{-6}$ $-16x^{-4}$…
timed problem score: 1/10 current time: 24.4 $\frac{d}{dx}(4x^{-5})$ answer $-\frac{2}{3}x^{-6}$ $-16x^{-4}$ $-x^{-4}$ $-20x^{-6}$
Answer
Answer:
D. $-20x^{-6}$
Explanation:
Step1: Recall power - rule for differentiation
The power - rule states that if $y = ax^n$, then $\frac{dy}{dx}=anx^{n - 1}$, where $a$ is a constant and $n$ is a real number.
Step2: Identify $a$ and $n$
For the function $y = 4x^{-5}$, we have $a = 4$ and $n=-5$.
Step3: Apply the power - rule
$\frac{d}{dx}(4x^{-5})=4\times(-5)x^{-5 - 1}$.
Step4: Simplify the expression
$4\times(-5)x^{-5 - 1}=-20x^{-6}$.