Get the answer to "Find the derivatives of the functions y=(5−2x)−3+18(2x+1)4"

Efan Halliday

Answered question

2021-09-20

Find the derivatives of the functions

y = {(5 - 2 x)}^{- 3} + \frac{1}{8} {(\frac{2}{x} + 1)}^{4}

Answer & Explanation

Ezra Herbert

Skilled2021-09-21Added 99 answers

Step 1
Here given
$y = {(5 - 2 x)}^{- 3} + \frac{1}{8} {(\frac{2}{x} + 1)}^{4}$
Step 2
Now, differentiate the given function x with respect to x
$\frac{d y}{d x} = \frac{d}{d x} {{(5 - 2 x)}^{3} + \frac{1}{8} {(\frac{2}{x} + 1)}^{4}}$
$\Rightarrow \frac{d y}{d x} = \frac{d}{d x} {(5 - 2 x)}^{- 3} + \frac{1}{8} \frac{d}{d x} {(\frac{2}{x} + 1)}^{4}$
$\Rightarrow \frac{d y}{d x} = - 3 {(5 - 2 x)}^{- 4} \frac{d}{d x} (5 - 2 x) + \frac{4}{8} {(\frac{2}{x} + 1)}^{3} \frac{d}{d x} (\frac{2}{x} + 1)$
$\Rightarrow \frac{d y}{d x} = - 3 {(5 - 2 x)}^{- 4} (- 2) + \frac{4}{8} {(\frac{2}{x} + 1)}^{3} {2 \frac{d}{d x} (\frac{1}{x}) + \frac{d}{d x} (1)}$
$\Rightarrow \frac{d y}{d x} = 6 {(5 - 2 x)}^{- 4} + \frac{1}{2} {(\frac{2}{x} + 1)}^{3} (\frac{2}{x^{2}})$
$\Rightarrow \frac{d y}{d x} = 6 {(5 - 2 x)}^{4} + (\frac{1}{x^{2}}) {(\frac{2}{x} + 1)}^{3}$

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