Question

find the indicated derivative. f(u)=8u^{0.4}-6u^{2.4} f(u)=□

Explanation:

Step1: Apply power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the first term $8u^{0.4}$, where $a = 8$ and $n = 0.4$, its derivative is $8\times0.4u^{0.4 - 1}=3.2u^{- 0.6}$. For the second term $-6u^{2.4}$, where $a=-6$ and $n = 2.4$, its derivative is $-6\times2.4u^{2.4 - 1}=-14.4u^{1.4}$.

Step2: Combine the derivatives of the terms

$f^\prime(u)$ is the sum of the derivatives of the individual terms in $f(u)$. So $f^\prime(u)=3.2u^{-0.6}-14.4u^{1.4}$.

Answer:

$3.2u^{-0.6}-14.4u^{1.4}$