find the derivative of the function. f(u)=5u^0.6 - 3u^2.8 f(u)=

Explanation:

Step1: Recall power - rule

The power - rule for differentiation is $\frac{d}{du}(au^n)=nau^{n - 1}$, where $a$ is a constant and $n$ is a real number.

Step2: Differentiate the first term

For the term $5u^{0.6}$, using the power - rule, we have $\frac{d}{du}(5u^{0.6})=0.6\times5u^{0.6 - 1}=3u^{- 0.4}$.

Step3: Differentiate the second term

For the term $-3u^{2.8}$, using the power - rule, we have $\frac{d}{du}(-3u^{2.8})=2.8\times(-3)u^{2.8 - 1}=-8.4u^{1.8}$.

Step4: Combine the derivatives

$f^{\prime}(u)=\frac{d}{du}(5u^{0.6}-3u^{2.8})=\frac{d}{du}(5u^{0.6})-\frac{d}{du}(3u^{2.8}) = 3u^{-0.4}-8.4u^{1.8}$.

Answer:

$3u^{-0.4}-8.4u^{1.8}$