"Find all derivatives of the function y=1/2x−3." was answered by our experts

Jaden Easton

Answered question

2021-10-12

Find all derivatives of the function y=1/2x−3.

Answer & Explanation

Ezra Herbert

Skilled2021-10-13Added 99 answers

Step 1
The given function

y = \frac{1}{2 x - 3}

.
Obtain the derivatives as follows.
Step 2

y = \frac{1}{2 x - 3}

y^{'} = \frac{- 2}{{(2 x - 3)}^{2}} = \frac{{(- 1)}^{1} 2^{1} (1!)}{{(2 x - 3)}^{1 + 1}}

y^{″} = \frac{- 2 (- 2) (2)}{{(2 x - 3)}^{2}} = \frac{{(- 1)}^{2} 2^{2} (2!)}{{(2 x - 3)}^{2 + 1}}

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

.
.
.

y^{(n)} = \frac{{(- 1)}^{n} 2^{n} (n!)}{{(2 x - 3)}^{n + 1}}

Thus, all the derivative is

y^{(n)} = \frac{{(- 1)}^{n} 2^{n} (n!)}{{(2 x - 3)}^{n + 1}}

where

n \in N

.

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