Question

Va rog sa rezolvati urmatoarele probleme:

Answer 1

Punctul A)

Se aplica formula de derivare:

$\boxed{(x^n)' = n \cdot x ^{(n-1)}}$

$\displaystyle\\f(x) = 5x^4 - 6x^3 + 3x - 4 \\ \\f'(x) = 5 \cdot 4 x ^3 - 6 \cdot 3 x^2 + 3 \\ \\f'(x) = 20x^3 - 18x^2 + 3$

Ne amintim!

• x' = 1, ∀ x ∈ R
• c' = 0, ∀ c = constantă   (ex: 13, ln 2, ∛5)

Punctul B)

Se aplica formula de derivare:

$\boxed{\left(\frac{f}{g}\right)' = \frac{f' \cdot g - g' \cdot f}{g^2}}$

$\displaystyle\\f(x) = \frac{x^2-3}{x-4} \\ \\f'(x) = \frac{(x^2-3)' \cdot (x-4) - (x^2-3) \cdot (x-4)'}{(x-4)^2} \\ \\f'(x) = \frac{2x \cdot (x-4) - (x^2 -3) \cdot 1}{x^2 - 8x +16} \\ \\f'(x) = \frac{2x^2 - 8x - x^2 + 3}{x^2 - 8x + 16} \\ \\f'(x) = \frac{x^2 - 8x + 3}{x^2 - 8x + 16}$

Succes!