Question

find g(w) if g(w) = \frac{2}{5w^{4}}+7\sqrt4{w}.
g(w) =

Explanation:

Step1: Rewrite the function

Rewrite $G(w)=\frac{2}{5w^{4}}+7\sqrt[4]{w}$ as $G(w)=\frac{2}{5}w^{- 4}+7w^{\frac{1}{4}}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$.
For the first term $\frac{2}{5}w^{-4}$, its derivative is $\frac{2}{5}\times(-4)w^{-4 - 1}=-\frac{8}{5}w^{-5}$.
For the second term $7w^{\frac{1}{4}}$, its derivative is $7\times\frac{1}{4}w^{\frac{1}{4}-1}=\frac{7}{4}w^{-\frac{3}{4}}$.

Step3: Combine the derivatives

$G^\prime(w)=-\frac{8}{5w^{5}}+\frac{7}{4w^{\frac{3}{4}}}$.

Answer:

$-\frac{8}{5w^{5}}+\frac{7}{4w^{\frac{3}{4}}}$