"Find an equation for the nth derivative of..." was answered by students like you

sodni3

Answered question

2021-11-10

Find an equation for the

n^{t h}

derivative of

\frac{x}{1 + x}

.

Answer & Explanation

hesgidiauE

Skilled2021-11-11Added 106 answers

Step 1
given:
the given expression is

\frac{x}{1 + x}

.
Step 2
find the

n^{t h}

derivative of the function as follows.

y = \frac{x}{1 + x}

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

y^{″} = \frac{- 2}{{(1 + x)}^{3}}

y^{‴} = \frac{6}{{(1 + x)}^{4}}

...=...

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

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

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