3 years ago

Differentiate (4x+5)/(3x^2+2)^3

Mathematics

1 answer:

Romashka [77]3 years ago

3 0

Answer:

(-60x - 90x + 8) / (3x^2 + 2)^4 or you could write it as

2( -30x - 45x + 4) / (3x^2 + 2)^4

Step-by-step explanation:

Using the Quotient rule:

d(u/v) = (vdu - udv) / v^2

We have:

[3x^2 + 2)^3 * 4 - (4x + 5) * 3 (3x^2 + 2)^2 * 6x] / (3x^2 + 2)^6

= 4(3x^2 + 2) - 18x(4x + 5) / (3x^2 + 2)^4

= (12x^2 + 8 - 72x^2 - 90x ) / (3x^2 + 2)^4

= (-60x - 90x + 8) / (3x^2 + 2)^4

= 2( -30x - 45x + 4) / (3x^2 + 2)^4

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Differentiate (4x+5)/(3x^2+2)^3​

Differentiate (4x+5)/(3x^2+2)^3