"Find the derivatives of the functions y=20(3x−4)14(3x−4)−15" was answered by our community

Joyce Smith

Answered question

2021-12-10

Find the derivatives of the functions

y = 20 {(3 x - 4)}^{\frac{1}{4}} {(3 x - 4)}^{- \frac{1}{5}}

Answer & Explanation

Esther Phillips

Beginner2021-12-11Added 34 answers

Step 1
Given:

y = 20 {(3 x - 4)}^{\frac{1}{4}} {(3 x - 4)}^{- \frac{1}{5}}

Step 2
Simplification:

y = 20 {(3 x - 4)}^{\frac{1}{4}} {(3 x - 4)}^{- \frac{1}{5}}

y = 20 {(3 x - 4)}^{\frac{1}{20}}

Step 3
Solution:

y = 20 {(3 x - 4)}^{\frac{1}{20}}

\frac{d y}{d x} = 20 (\frac{1}{20}) {(3 x - 4)}^{\frac{1}{20} - 1} \frac{d}{d x} (3 x - 4)

\frac{d y}{d x} = {(3 x - 4)}^{\frac{- 19}{20}} (3)

\frac{d y}{d x} = 3 {(3 x - 4)}^{\frac{- 19}{20}}

\frac{d y}{d x} = \frac{3}{{(3 x - 4)}^{\frac{19}{20}}}

\frac{d y}{d x} = \frac{3}{{(3 x - 4)}^{\frac{19}{20}}}

Step 4
Answer:

\frac{d y}{d x} = \frac{3}{{(3 x - 4)}^{\frac{19}{20}}}

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