Expert Answer to "Find all derivatives of the function y=12x−3"

sjeikdom0

Answered question

2021-06-07

Find all derivatives of the function

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

Aniqa O'Neill

Skilled2021-06-08Added 100 answers

Step 1
We find first few derivatives using the power rule and chain rule

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

y^{(1)} = - 1 {(2 x - 3)}^{- 2} (2) = - 2 {(2 x - 3)}^{- 2} = (- 1) (2) (1!) {(2 x - 3)}^{- 2}

y^{(2)} = 4 {(2 x - 3)}^{- 3} (2) = 8 {(2 x - 3)}^{- 3} = {(- 1)}^{2} (2) (2!) {(2 x - 3)}^{- 3}

y^{(3)} = - 12 {(2 x - 3)}^{- 3} (2) = - 24 {(2 x - 3)}^{- 4} = {(- 1)}^{3} (2) (3!) {(2 x - 3)}^{- 4}

y^{(4)} = 36 {(2 x - 3)}^{- 3} (2) = 72 {(2 x - 3)}^{- 5} = {(- 1)}^{4} (2) (4!) {(2 x - 3)}^{- 5}

Step 2
Then we find a pattern for integer n

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

Answer:

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

Jeffrey Jordon

Expert2022-08-14Added 2605 answers

Answer is given below (on video)

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