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Calcola la seguente derivata:? y=(3x^3+4x+1)(3x^2+4)?

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Si deve calcolare la derivata prima del prodotto di due funzioni f(x) per g(x). Si deve ricorrere

alla regola di derivazione del prodotto di due funzioni:

D[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)

Quindi:

y' = (9x² + 4)(3x² + 4) + (3x³ + 4x + 1)(6x)

y' = 27x^4 + 36x² + 12x² + 16 + 18x^4 + 24x² + 6x

y' = 45x^4 + 72x² + 6x + 16

Ciao

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Secondo me fai prima a moltiplicare:

9x^5 +12x^3 +12x^3 +3x^2+16x+4=

9x^5+24x^3 +3x^2+16x+4.

Quindi la derivata è:

45x^4 +72x^2 +6x +16.

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Dovrai sapere che la derivata di f(x)g(x) = f'(x)g(x) + f(x)g'(x) pertanto :

(9x^2 + 4)(3x^2 + 4) + (3x^3 + 4x + 1)(6x)

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