find-the-indicated-higher-order-derivative-of-the-following-function-f-x-x-3-4x-5-4-f-x-iv-

Question Number 157836 by zakirullah last updated on 28/Oct/21

f i n d t h e i n d i c a t e d h i g h e r o r d e r d e r i v a t i v e

o f t h e f o l l o w i n g f u n c t i o n

f (x) = {(x^{3} + 4 x - 5)}^{4}, f {(x)}^{i v}

Answered by tounghoungko last updated on 29/Oct/21

f (x) = {(x - 1)}^{4} {(x^{2} + x + 5)}^{4}

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

+ 6 \frac{d^{2}}{{d x}^{2}} {((x - 1))}^{4} \frac{d^{2}}{{d x}^{2}} {(x^{2} + x + 5)}^{4} + 4 \frac{d}{d x} {((x - 1))}^{4} \frac{d^{3}}{{d x}^{3}} {(x^{2} + x + 5)}^{4}

+ 4 {(x - 1)}^{4} \frac{d^{4}}{{d x}^{4}} {(x^{2} + x + 5)}^{4}

= 24 {(x^{2} + x + 5)}^{4} + 96 (x - 1) \frac{d}{d x} {(x^{2} + x + 5)}^{4} + 72 {(x - 1)}^{2} \frac{d^{2}}{{d x}^{2}} {(x^{2} + x + 5)}^{4}

+ 16 {(x - 1)}^{3} \frac{d^{3}}{{d x}^{3}} {(x^{2} + x + 5)}^{4} + 4 {(x - 1)}^{4} \frac{d^{4}}{{d x}^{4}} {(x^{2} + x + 5)}^{4}

Commented by zakirullah last updated on 03/Nov/21

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