Get the solution to "Find all derivatives of the function y=1/1−5x."

chillywilly12a

Answered question

2021-10-20

Find all derivatives of the function y=1/1−5x.

tabuordg

Skilled2021-10-21Added 99 answers

Step 1
Given function is

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

Differentiating both sides with respect to x ,repeatedly, we get

y^{'} = \frac{d}{d x} {(1 - 5 x)}^{- 1} = - {(1 - 5 x)}^{- 2} \frac{d}{d x} (1 - 5 x) = 5 (1!) {(1 - 5 x)}^{- 2}

y^{″} = \frac{d}{d x} 5 (1!) {(1 - 5 x)}^{- 2} = 5 (- 2) (1!) {(1 - 5 x)}^{- 3} \frac{d}{d x} (1 - 5 x) = 5^{2} (2!) {(1 - 5 x)}^{- 3}

y^{‴} = \frac{d}{d x} 5^{2} (2!) {(1 - 5 x)}^{- 3} = 5^{2} (- 3) (2!) {(1 - 5 x)}^{- 4} \frac{d}{d x} (1 - 5 x) = 5^{3} (3!) {(1 - 5 x)}^{- 4}

In general, nth derivative of given function is

y^{(n)} = 5^{n} (n!) {(1 - 5 x)}^{- (n + 1)}

Step 2
Ans: nth derivative of given function is

y^{(n)} = 5^{n} (n!) {(1 - 5 x)}^{- (n + 1)}

Jeffrey Jordon

Expert2022-08-13Added 2605 answers

Answer is given below (on video)

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