Question

find the indicated derivative.
$\frac{d}{du}(2u^{0.4}-6u^{2.6})$
$\frac{d}{du}(2u^{0.4}-6u^{2.6})=square$

Explanation:

Step1: Apply sum - difference rule

The derivative of a sum/difference of functions is the sum/difference of their derivatives. So, $\frac{d}{du}(2u^{0.4}-6u^{2.6})=\frac{d}{du}(2u^{0.4})-\frac{d}{du}(6u^{2.6})$.

Step2: Apply constant - multiple rule

The constant - multiple rule states that $\frac{d}{du}(cf(u)) = c\frac{d}{du}(f(u))$. So, $\frac{d}{du}(2u^{0.4}) = 2\frac{d}{du}(u^{0.4})$ and $\frac{d}{du}(6u^{2.6})=6\frac{d}{du}(u^{2.6})$.

Step3: Apply power rule

The power rule for derivatives is $\frac{d}{du}(u^n)=nu^{n - 1}$. For $n = 0.4$, $2\frac{d}{du}(u^{0.4})=2\times0.4u^{0.4 - 1}=0.8u^{- 0.6}$. For $n = 2.6$, $6\frac{d}{du}(u^{2.6})=6\times2.6u^{2.6 - 1}=15.6u^{1.6}$.

Step4: Calculate the result

$\frac{d}{du}(2u^{0.4}-6u^{2.6})=0.8u^{-0.6}-15.6u^{1.6}=\frac{0.8}{u^{0.6}}-15.6u^{1.6}$.

Answer:

$0.8u^{-0.6}-15.6u^{1.6}$