Question: "Derivatives Find and simplify the derivative of the..." - Plainmath

Cheyanne Leigh

Answered question

2021-10-10

Derivatives Find and simplify the derivative of the following functions

y = (2 \sqrt{x} - 1) {(4 x + 1)}^{- 1}

Answer & Explanation

Daphne Broadhurst

Skilled2021-10-11Added 109 answers

Step 1
Given function is

y = (2 \sqrt{x} - 1) {(4 x + 1)}^{- 1}

.
Step 2
Compute the derivative.

y^{'} = {(\frac{2 \sqrt{x} - 1}{4 x + 1})}^{'}

= \frac{(4 x + 1) {(2 \sqrt{x} - 1)}^{'} - (2 \sqrt{x} + 1) {(4 x + 1)}^{'}}{{(4 x + 1)}^{2}}

= \frac{(4 x + 1) (\frac{1}{\sqrt{x}}) - (2 \sqrt{x} + 1) (4)}{{(4 x + 1)}^{2}}

= \frac{\frac{4 x + 1 - 8 x + 4 \sqrt{x}}{\sqrt{x}}}{{(4 x + 1)}^{2}}

= \frac{1 - 4 x + 4 \sqrt{x}}{\sqrt{x} {(4 x + 1)}^{2}}

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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