Math, asked by vinaymore1642, 4 months ago

the nth derivative of 1/(x+2)^3​

Answers

Answered by mathdude500
1

Answer:

f(x) =  \frac{1}{ {(x + 2)}^{3} }  \\ </p><p>f'(x) =  -  \frac{3}{ {(x + 2)}^{4} }  =   {( - 1)}^{1}   \frac{3!}{2! {(x + 2)}^{1 + 3} }  \\ </p><p>f''(x) = ( - )( - ) \frac{3 \times 4}{ {(x + 2)}^{5} }  =   {( - 1)}^{2}   \frac{(2 + 2)!}{2! {(x + 2)}^{2 + 3} }\\ </p><p>f'''(x) = ( - )( - )( - ) \frac{3 \times 4 \times 5}{ {(x + 2)}^{6} } =   {( - 1)}^{3}   \frac{(3 + 2)!}{2! {(x + 2)}^{3 + 3} }</p><p>. \\ . \\ . \\ . \\ nth \: derivative \:  =  {( - 1)}^{n}  \frac{(n + 2)!}{2! {(x + 2)}^{n + 3} }

Answered by suman8615
0

Answer:

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

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