Question

32 pontos !!! Calcule as derivadas das tres funções a seguir

Answer 1

a

y' = 20x^4 + 3

b

y' = (27x^2 + 5)/(9x^3 + 5x)

c

y' = 6 × [(8x^3 + 3) . (2 + x + x^3) +

(2x^4 + 3x) . (1 + 3x^2)]

Answer 2

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$\sf y=4x^5+3x-3^{9+2}\\\sf y=4x^5+3x-3^{11}\\\boxed{\sf\dfrac{dy}{dx}=20x^3+3}\\\sf y=\ell n(9x^3+5x)\\\sf\dfrac{dy}{dx}=\dfrac{1}{9x^3+5x}\cdot(27x^2+5)\\\boxed{\sf f'(x)=\dfrac{27x^2+5}{9x^3+5x}}\\\sf y=(6x^4+9x)(4+2x+2x^3)\\\sf\dfrac{dy}{dx}=(24x^3+9)(4+2x+2x^3)+(6x^4+9x)(2+6x^2)\\\sf\dfrac{dy}{dx}=48x^6+48x^4+114x^3+18x+36+36x^6+12x^4+54x^3+18x\\\sf\dfrac{dy}{dx}=84x^6+60x^4+168x^3+36x+36\checkmark$