Question

the nth derivative of 1/(x+2)^3​

Answer 1

Answer:

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

Answer 2

Answer:

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